Aleksander Borisenko

Publications

Books

  1. Analytical geometry (co-author Ushakova L.N.).// Publ. "OsnovaM,Kharkov,1993,191 p.
  2. Differential Geometiy and Topology. Publ."Osnova", Kharkov, 1995,300 р.
  3. Intrinsic and extrinsic geometry of multidimensional submanifolds// Moskow, Publish house "Examen", 2003. 670p.
  4. An introduction to Hamilton and Perelman's work on the conjectures of Poincare and Thurston, (co-authors E. Cabezas-Rivas, V. Miquel-Molina), Matematiques, 3,2 (2006), 1-150 p.

Articles

  1. On spherical image of a shortest line on a convex surface.// Ukr.Geom.Sb.,1971,V.10,P.ll-12.
  2. On the structure of hypersurfaces with a zero spherical image of hausdorf measure.// Ukr.Geom.Sb.,1972,V.12,P.36-45.
  3. On the class of Riemannian spaces of a strong negative curvature.//Ukr.Geom.Sb.,1973,V.13,P.15-18.
  4. On the structure of 1-dimensional surfaces with a degenerated second fundamental form in n-dimensional Euclidean space.// Ukr.Geom.Sb.,1973,V.13,P.18-27.
  5. On the structure of a continuous surface, containing straight line.// Ukr.Geom.Sb.,1973,V.14,P.21-24.
  6. On complete surfaces in the spaces of a constant curva¬ture.// Ukr.Geom.Sb., 1974,V. 15,P.8-16.
  7. On compact surfaces of nonpositive extrinsic curvature in the spherical space.// Ukr.Geom.Sb.,1975,V.17,P.33-35. .
  8. On straight lines on the complete noncompact 2-dimensional Riemannian manifold.// Ukr.Geom.Sb., 1975,V.17,P.35-44.
  9. On the Euler characteristic of compact surfaces of the negative extrinsic curvature in Riemannian space.// Ukr.Geom.Sb.,1975,V.18,P.20-25.
  10. On saddle surfaces in the spherical space.// Ukr.Geom.Sb., 1975,V.18,P.25-27
  11. On compact surfaces of negative extrinsic curvature in Riemannian space.// Ukr.Geom.Sb., 1976,V.19,P.9-11
  12. On isometric imbedding of the pseudoriemannian spaces of a constant curvature.// Ukr.Geom.Sb., 1976,V. 19, P.ll-19.
  13. A class of a Riemannian space./ Mathem.EncycIopedia, 1979,V.l.
  14. Complete 1-dimensional surfaces of nonpositive extrinsic curvature in a Riemannian space.// Matematicheskii Sbornik USSR,1977,V.104(146),No 4(12),P.559-577. (English translation Mathematics of the USSR-Sbornik, 1977, V.33, No 4,P. 485-499)
  15. The correction to the paper "On a structure of huper- surfaces with a zero spherical of Hausdorf measure".// Ukr.Geom.Sb.,1978,V.21,P.141.
  16. ACurvature./Encyclopaedia(UKRAINE),1980.
  17. On Pontryagin classes of compact surfaces in a spherical space.//Ukr.Geom.Sb., 1980, V.23,P.24-30.
  18. On compact surfaces with a field of principal directions in a spherical space.// Ukr.Geom.Sb.,1980,V.23,P.30-32.
  19. On surfaces of nonpositive extrinsic curvature in a spaces of a constant curvature.// Mathematicheskii Sbornic USSR,1981,V.l 14(156),No 3,P.339-354. (English translation Mathematics of the USSR-Sbornik, 1982, V. 42, No 3, P. 297-310)
  20. Ecstrinsically geometric and topological properties of parabolic and saddle surfaces in rank one summetric spaces.// Soviet.Math.Dokl.,1981,V.23,No 2. 783-788
  21. On parabolic surfaces in the Euclidean spaces.// Ukr.geom.Sb., 1982, V.25,P.3-6.
  22. On a grapfical minimal surfaces.// Ukr.geom.Sb., 1982, V.25,P.6-8.
  23. On the extrinsic geometric properties of parabolic surfaces and topological properties of saddle surfaces in Symmetric spaces of rank 1.// Math.Sb.USSR,1981, V.l 16(158),P.440-457. (English translation Mathematics of the USSR-Sbornik, 1983, V44(3), P.401-415)
  24. The surfaces with a degenerated spherical image (co-author Lisitsa V.T.).// Ukr.Geom.Sb.,1984,V.27, P. 12-22.
  25. Construction of the graphs (co-author Jakuba M.A.)./ Preprint,Kharkov State University, 1984.
  26. On complete parabolic surfaces in a Euclidean space.// Ukr.Geom.Sb.,1985,V.28,P.8-19.
  27. On some classes of manydimensional surfaces.// Ukr.Geom.Sb.,1986,V.29,P.5-12. (English translation Journal of Soviet Mathematics, 1990, V. 51, №2, p. 2191-2196)
  28. On cylindercity of the tangent bundles of the strong parabolic metrics and the strong parabolic surfaces (co-author Yampol'sky A.L.).// Ukr.Geom.Sb.,1986, V.29,P. 12-32. (English translation Journal of Soviet Mathematics, 1990, V.51,№ 2, p. 2197-2212)

  29. On algebraical surfaces which are given by a homo-geneons polynomial (co-author Nikolaevsky J.A.).// Ukr.geomSb.,1987,V.30,P.3-10. (English translation Journal of Soviet Mathematics, October 1990, Volume 51, Issue 5, pp 2497-2502)

  30. Sectional curvature of the Sasaki metric T M (coauthor Yampol'sky AX.).//Ukr.Geom.Sb.,l 987,V.30, P.10-18. (English translation Journal of Soviet Mathematics, October 1990, Volume 51, Issue 5, pp 2503-2508)

  31. On the Sasaki metric of tangent and normal bundles (co-author Yampolsky A.L.).// Soviet Math. Dokl., 1987,V.294,No 1, P. 19-23.

  32. On extremal properties of compact surfaces of nonpo-sitive extrinsic curvature.// Soviet Math. Dokl., 1987, V.133,Nol,pJ 12-126

  33. On the Sasaki metric of tangent and normal bundle of the submanifold in a Riemannian manifold (co-author Yampolsky A.L.).// Mathematicheskii Sbornik USSR, 1987, V.l 34(176),No 2,P.158-176. (English translation Mathematics of the USSR-Sbornik, 1989, V62, №1, P. 157-175)

  34. On extremal properties of compact parabolic surfaces in a Riemannian space.// Matematicheskii Sbornik USSR, 1987,V.133(175),No l,P.l 12-126. (English translation Mathematics of the USSR-Sbornik, 1988, V61,№1, P.l 13-127)

  35. On normal curvature and topological structure of the manydimensional surfaces in the spherical space.// Ukr.Geom.Sb.,1988,V.31,P.3-14 (English translation Normal curvature and the topological structure of multidimensional surfaces in a spherical spaceW Journal of Soviet Mathematics March 1991, Volume 54, Issue 1, pp 675-678)

  36. On a characteristical property of the manydimensional cylindrical surfaces (co-author Ushakov V.G.).//Ukr.Geom.Sb.,1988,V.31,P.19-25. (English translation A characteristic property of multidimensional cylindrical surfacesW Journal of Soviet Mathematics, March 1991, Volume 54, Issue 1, pp 678-683)

  37. On surfaces for which the Chern-Lashof curvature is equal to the area of the Grassmanian image.//   Mathematicheskie Zametki,1989,V.46,№ 3JP.9-11. (English translation Mathematical Notes, 1989, V.46, №3, p. 687-688)

  38. The point-wise classification of 3 -dimensional surfaces by the Grassmanian image(co-author NikolaevskyJ.A.).//Ukr.Geom.Sb.,1989,V.32,P.17-27. (English translation Classification of the points of three-dimensional surfaces according to the Grassmann imageW Journal of Soviet Mathematics April 1992, Volume 59, Issue 2, pp 697-709)

  39. On surfaces with maximal curvature along the Grassmanian image (co-author Nikolaevsky J.A.).// Mathematicheskie Zametki,1990,V.48,No 3,P. 12-20. (English translation Mathematical Notes, V.48,No 3,P. 880-885)
  40. Affine classification of the multidimensional surfaces points.// Sibirskii Math. Journal, 1990,V.31,No 3,P. 19-30. (English translation Siberian Mathematical Journal, 1990, V. 31, №3, p. 379-387)
  41. On cylindrical multidimensional surfaces in Lobachevsky space.// Ukr.Geom.Sb.,1990,V.33, P. 18-27.(English translation Cylindrical multidimensional surfaces in Lobachevsky spaceW Journal of Soviet Mathematics, February 1991, Volume 53, Issue 5, pp 474-480)
  42. On isometric imbedding of the strongly parabolic metrics into the class of strongly parabolic surfaces, (co-author Ushakov V.G.)// Ukr.Geom.Sb.,1990,V.33,P.27-36. (English translation The isometric immersion of strongly parabolic metrics in the class of strongly parabolic surfacesW Journal of Soviet Mathematics, February 1991, Volume 53, Issue 5, pp 481-487)
  43. On a structure of complete noncompact convex hypersurface in E with bound mean curvature (co-author Sergienko L.N.).// Ukr.Geom.Sb.,1991, v.34,P.8-9. (English translation The structure of an infinite, complete, convex hypersurface inE 4 with bounded mean curvatureW Journal of Mathematical Sciences, March 1994, Volume 69, Issue 1, pp 829-830)
  44. On the rigidity of the multidimensional submanifolds by the Grassman image.// Mathematicheskie Zametki, 1992,V.51, No 1, P.8-15. (English translation Mathematical Notes, 1992,V.51,Nol,P.6-ll)
  45. On isometric submanifolds of arbitrary codimension in Euclidean spaces with the same Grassmanian image.// Mathematicheskie Zametki, 1992, V.52,No 4,P.29-34. (English translation Mathematical Notes, 1992,V.52,No4,P. 1012-1015)
  46. On Liuvill's type theorem for the equation of special Lagrange submanifolds.//Mathematicheskie Zametki, 1992, V.52,No 5,P.22-25. (English translation Mathematical Notes, 1992, V.52,No5,P. 1094-1096)
  47. On the structure of parabolic Kahler submanifolds in Kahler manifolds (co-author Ostroumov S.A.)// Journal of Mathematical Physics, Analysis, Geometry 1994,V.l,No 1, P.60-77.
  48. On the cylindricity of complete strongly parabolic Kahler submanifolds in complex Hermitian space (co-author Ostroumov S.A.)// Journal of Mathematical Physics, Analysis, Geometry,1995,V.2,No.3/4,P.284-295.
  49. On compact submanifolds of nonpositive extrinsic curvature in Riemannian space // Math. Zametki, 1996, V.60,N 1, 3-10. (English translation Mathematical Notes, 1996, V.60,N1„P. 3-7)
  50. Convex surfaces in Lobachevsky space (co-author Vlasenko D.) // Matem. Fiz., Anal., Geometriya, Kharkov,l 997,V.4,No.3,P. 1 -8.
  51. Saddle submanifolds in Riemannian space (co-authors K.Tenenblat, M.Rabelo) // Geometriae Dedicata,1997, V.67(2),P.233-243.
  52. Foliations of negative extrinsic curvature in a Riemannian space // Matem. Zametki, Moskow,1997, V.67,No.5,P.673-676. (English translation Mathematical Notes, 1997, V.67,No.5,P. 562-565)
  53. Total curvature of convex hypersurfaces in hyperbolic space (co-author V.Miquel)// Ilinois Journal of Mathematics,1999,V.43,No.l,P.l-17.
  54. Strongly parabolic timelike submanifolds of Minkovsky space (co-authors Rabelo M., Tenenblat K.) // Journal of Mathematical Physics, Analysis, Geometry, Kharkov,1999,V.6,No.l-2,P.l-12. Compact Hopf hypersurfaces // Dokl. NAN Ukr.,1999,No.8, P.13-17.
  55. Asymptotic behavior of volume of convex sets in Adamar manifold (co-author D.Vlasenko)// Journal of Mathematical Physics, Analysis, Geometry, Kharkov, 1999,V.6,No.3-4,P.223-233
  56. Explicit saddle surfaces in spherical space // Uspechi Mat.Nauk, 1999, V.54, N.5, P.151-152. (English translation Russian Mathematical Surveys, 1999, 54:5,1021-1022)
  57. Local convex hypersurfaces in Hadamard manifolds // Mat. Zametki, 2000, V.67, N.4, P.498-507. (English translation Mathematical Notes, 2000, V.67, N.4, P.425 - 432)
  58. About volumes of convex bodies in manifolds of nonpositive sectional curvature (co-author D.Vlasenko)// Dopovidi National Acad. Nauk Ukr.,2000,No.6,P.10-14
  59. Relation between area and volume for lambda-convex sets in
  60. Hadamard manifolds (co-authors E.Gallego and A.Reventos) // Differential geometry and its Applications, 2001, V.14, p.267-280.
  61. On the global structure of Hopf hypersurfaces in a complex space form // Illinois Journal of Mathematics, 2001, V.45, N.l,p.265-277
  62. Mathematics and Society // Universitates, Kharkov, 2001, N.l,p.l8-26.
  63. The structure of Hopf hypersurfaces in Sasaki and 3 -Sasaki space forms (co-author V.Miquel) // Proceedings of Toponogov's conference "Geometry and application", Novosibirsk (13-16 Marten 2000), Mathematics Institute, 2001, p. 17-25.
  64. A quantitative estimation of representative volume in hydrodynamics (co-author Nemets K. A., Yampolsky E.A.) // Bulletin of Kharkov National
    University, Ser. Geology-Geography-Economy, 2001, N.521, p.93-100.
  65. Comparasion Theorem on Hypersurfaces in Hadamard Manidold ( co-author V.Miquel ) // Differential Geometry and its Applications, 2002, v. 17, p. 191-202
  66. Convex sets in Hadamard manifold,//
    Diffferential Geometry and its Applications, 2002, v. 17, p.l 11-121
  67. Classification of two-dimensional and three-dimensional surfaces points on Grassmann image// Journal of Mathematical Physics, Analysis, Geometry, 2002, V.. 9, N.4, p.572-594
  68. The prominent mathematic of XX century// Universitates, 2003, № 4, p. 55-60
  69. Structure of Hopf Hypersurfaces in Sasakian and 3-Sasakian space forms// Siberian Advances in Mathematics, 2003, v,13,N.3,p.54-61
  70. Complex submanifolds with extremal curvature (co-author Leybina O.V.)// Dopovidi of National Academy of Sciences of Ukraine, Ser. Mathematics, 2004, N.10.
  71. Extremal properties of Lobachevsky space (co-author Vlasenko DJ.)// Dopovidi of National Academy of Sciences of Ukraine, Ser. Mathematics, 2004, N.12.
  72. Absolute Chern-Lashof curvature of complex submanifolds and the volume of Grassmann image (co-author Leybina O.V.) // Math. Zametki, 2007, v.81, №5 p. 666-675 (English translation Mathematical Notes, 2007, V.81, №5, p. 596-604)
  73. Convex hypersurfaces in Hadamard manifolds// Complex Contact and Symmetric manifolds, Ser. Progress in Mathematics, 2005, v.234, p.50-68
  74. Geometry of submanifolds and Riemannian spaces,// Fundamental guiding line of science (Mathematics, Informatics, Mechanics), Collections of articles, Kyiv, Publish House "Academperiodika", 2005, p. 43-57
  75. Compact spacelike surfaces in the 3 -dimensional de Sitter space// Journal of Mathematical Physics, Analysis, Geometry, 2006, v. 2, № 1, p. 3-8
  76. Pogorelov is the mathematician of wonderfull power, // Journal of Mathematical Physics, Analysis, Geometry, 2006, № 3,231-268
  77. Hypothesis of Poincare and Thurston, Universitates, 2006, №3, p.24-33
  78. About topology of saddle submanifolds, (co-author V.Rovenski), Diff. Geom. and its Appl 2007. - Vol. 25. - № 2. p. 220-233
  79. Some comparison theorems in Finsler-Hadamard manifolds, (co-author Olin E.L.), Journal of Mathematical Physics, Analysis, Geometry, №3, 2007, p. 298-312
  80. Chern-Lashof Absolute Curvature of Complex Submanifolds and Volumes of Grassmann Images, (co-author O.V. Leibina), Mat. Zametki, 2007, V.81, №5, p. 666 - 675 (English translation Mathematical Notes, 2007, V.81, №5, p. 596-604)
  81. About connection between the volume and the area of balls in Finsler-Hadamard manifolds (co-author E.Olin) Report of NAS of Ukraine, 2007, No6, p. 1 - 4
  82. Asymptotic properties of Hilbert geometry (co-author E.Olin), Journal of Mathematical Physics, Analysis, Geometry, 2008, V.4, No3, p. 327 - 345
  83. A. M. Lyapunov (1857-1918) (On his 150th birthday). Visnyk, seriya "Mat.,Prikl.Mat I Mech." 2008, No790, p. 41-52
  84. Alexei Mihajlovich Lyapunov (On his 150th birthday), Universitates, №16, 2008, c.84- 91
  85. Outstanding mathematician of the XX century, Universitates, 2008, c. 125-130
  86. On Isometric Immersion of Nilmanifolds in Euclidean space, Mat. Zametki, 2010, V.87, №l,p. 130-132 (English translation Mathematical Notes, 2010, V.87, №1, p. 122-124)
  87. Some comparison theorems in Finsler and Minkowski spaces, Acta Math. Academiae Paedagogicae Nyiregyhaziensis, 2010, Vol. 26, No. 2, p. 231-245
  88. The Global Structure of Locally Convex Hypersurfaces in Finsler-Hadamard Manifolds (co-author E.Olin), Mat.Zametki, 2010, V.87, №2, p. 163 - 174 (English translation Mathematical Notes, 2010, V.87, №2, p. 155-164)
  89. Gaussian mean curvature flow (co - author V.Miquel), Journal of Evolution Equations 10(2010), 413-423
  90. One-to-One Projectability of Closed Surfaces in a Spherical Space, Mat. Zametki, 2011, V.89, №1, p. 120 -121 (English translation Mathematical Notes, 2011, V.89, №1, p. 131-132)
  91. Surfaces in the Three-Dimensional Heisenberg Group on Which the Gauss Map Has Bounded Jacobian (co-author E.Petrov), Mat.Zametki, 2011, V.89, №5, p. 794 - 796 (English translation Mathematical Notes, 2011, V.89, №5, p. 746-748)
  92. Curvatures of hyperspheres in the Hilbert geometry (co-author E.Olin), Reports of NAS of Ukraine, No4, 2011, p. 15 - 19.
  93. About an angle comparison theorem for closed curves (co-author K.Drach), Reports of NAS of Ukraine, No6,2011, p. 7 - 11.
  94. About the curvature of some family of plane curves (co-author M.Golitsyna), Reports of NAS of Ukraine, No7, 2011, p. 12 - 16.
  95. On the 90th Anniversary of Geometry Department of Kharkiv University, Universitates №1(2011), 58-66
  96. Curvature hypersphere in Hilbert Geometry (co-author E.Olin) Pacific Journal of Mathematics, 2012, V.254, No2, p. 257-273.
  97. On the total curvature of curves in a Minkowski space (co-author Keti Tenenblat), Israel Journal of Mathematics, 2012, V.191, N.2, p. 755 - 769
  98. Mean curvature flow of graphs in warped products (co-author Vicente Miquel), Transactions of the American Mathematical Society, 2012, N. 364, p. 4551-4587
  99. About flag curvature of two-dimensional surfaces in three-dimensional Randers spaces (co-author S. Myroshnichenko) Reports of NAS of Ukraine, 2012, No11
  100. About the sphericity of hypersurfaces with normal curvature bounded from below (co author K. Drach), Matematicheskii Sbornik, 2013, V.204, No11 (English translation Sbornik: Mathematics, 2013, 204:11, 1565-1583)
  101.  А. А. Борисенко, К. Д. Драч, «Изопериметрическое неравенство для кривых с ограниченной снизу кривизной», Матем. заметки, 95:5 (2014), 656–665. Englishtranslation: Math. Notes, 2014, vol. 95, №5, 14-22
  102. Alexander Borisenko, Kostiantyn Drach, Extreme Properties of Curves with Bounded Curvature on a Sphere, Journal of Dynamical and Control Systems 2014., vol. 20, №1. DOI: 10.1007/s10883-014-9221-z.
  103. Aleksander Borisenko and Vladimir Rovenski, Gaussian Mean Curvature Flow for Submanifolds in Space Forms, Lecture Notes in Math., p. 39-50, serie: Geometry and Algebra (Springer Proceedings in Mathematics & Statistics), Vol. 72, 2014, pp. 243.
  104. А. А. Борисенко, “О цилиндричности подмногообразий, содержащих прямую, в пространстве Минковского”, Матем. сб., 205:7 (2014), 25–42. Englishtranslation: Sb. Math
  105. А. А. Борисенко, С. В. Мирошниченко, О полной кривизне кривых в несимметричных пространствах Минковского, Доповіді НАН України, 2014, №10, с. 7 – 11
  106. Alexander Borisenko, Kostiantyn Drach, Geometry of hypersurfaces with bounded normal curvature, The International Congress of Mathematicians, 2014, Short Communications, Seoul, Korea, Aug. 2014, Seoul, ICM 2014, pp. 116-117
  107. Borysenko Oleksandr Andriyovych, About cylindricity of Submanifolds with straight line in Minkowsky Space, 13th Serbian Mathematical Congress Book of Abstracts, May 22-25, 2014, Vrnjačka Banja, Serbia, p. 77
  108. Теорема сравнения для опорных функций гиперповерхностей (co author K. Drach) НАН України, Доповіді НАН України, № 3, 2015, 11-15
  109.  Immersion of Kähler manifolds in the class of convex submanifolds Springer, Математические заметки, 100, 4, 2016, 501-509; English translation: Mathem. Notes, 100, 3-4, 2016, 526-530
  110. Reverse isoperimetriec inequality in two-dimensional Alexandrov spaces American Mathematical Society, Proceedings of the AMS, 145, 2017, 4465-4471
  111. Видатний математик, просвітитель і організатор науки НАН України, Вісник НАН України, № 11, 2017, 86-91
  112. About the structure of multidimensional submanifolds with metric of revolution in Euclidean space, Journal of Mathematical Physics, Analysis, Geometry, 2018, № 4

Огляди

  1. Grassman manifolds and Grassmanian image of subma-nifolds (co-author Nikolaevsky J.A.).// Uspekhi Math. Nauk,1991,V.46,No 2(278),P.41-83 (English translation Math. Surveys,v.46,No 2, 1991, p.45-94)
  2. Riemannian geometry for Bundles (co-author Yampol'sky AX.).// Uspekhi Math. Nauk,1991,V.46,No 6(282), P.5 1 -96 (English translation Russian Math. Surveys,v.46, No6,1991,p.55-106)
  3. Extrinsic geometry strongly parabolic multidimensional submanifolds // Uspekhi Math. Nauk,1997,V.52,No.6,P.3-52. (English translation Russian Mathematical Surveys, 1997, 52:6, 1141-1190)
  4. Extrinsic geometry parabolic and saddle multidimensional submanifolds // Uspekhi Math. Nauk,1998,V.53,No.6,P.3-50 (English translation Russian Mathematical Surveys, 1998, 53:6, 1111-1158)
  5. Isometric immersions space forms in Riemannian and pseudoriemannian spaces of constant curvature // Uspekhi Mat. Nauk, 2001, V.56, N.3, p.3-78 (English translation Russian Mathematical Surveys, 2001, 56:3,425^4-97)