Aleksei Pogorelov

Alexei Vasilyevich Pogorelov (Russian Алексей Васильевич Погорелов, Ukrainian Олексій Васильович Погорєлов / Oleksiy Wassylowytsch Pohorjelow; born March 2, 1919 in Korotscha, Belgorod Oblast, † December 17, 2002 in Moscow) was a Soviet mathematician of Russian descent, which dealt with geometry.

Life and work

1937 to 1941 he studied at the University of Kharkov, and then until 1945 at the Zhukowsky - Air Force Academy in Moscow. After the war he continued to study in Moscow with Nikolai Efimov and Alexander Danilovich Aleksandrov. In 1947 he habilitated in Moscow and returned to the University of Kharkiv, where he obtained the chair of geometry. Since 1960 he worked at the Institute for Low Temperature Physics in Kharkov as head of the geometry in the mathematical department.

Pogorelov was mainly concerned with geometry, for example, the geometry of convex bodies, Geometric theory of Monge - Ampere equations and Hilbert's fourth problem, but also in applied mathematics (such as the theory of thin shells in statics, which he also examined in experiments) and even as an engineer with refrigeration ( cryogenic turbo-generators ). In addition to monographs, he also wrote a popular in Russia geometry - school textbook (1972). Pogorelov proved the regularity of convex surfaces if the metric is regular and the Gauss curvature positive.

In 1950 he was awarded the Stalin Prize ( State Award ), 1962 the Lenin Prize and in 1959 the Lobachevsky Medal. He was a member of the Soviet Academy of Sciences ( corresponding member since 1960, since 1976 a full member ) and the Ukrainian Academy of Sciences ( corresponding member since 1951, since 1960 a full member ).

Writings

  • Extrinsic geometry of convex surfaces, Providence, Rhode Iceland, American Mathematical Society 1973
  • Hilbert's fourth problem-, VHWinston, Washington, New York 1979
  • The Minkowski Multidimensional Problem, VHWinston, New York 1978
  • Topics in the theory of surfaces in elliptic space, Gordon and Breach 1961
  • A study of elliptic surfaces in space, New Delhi 1964
  • Unique determination of general convex surfaces, Akademie Verlag, Berlin 1956
  • The bending of convex surfaces, Akademie Verlag, Berlin 1957
  • Monge Ampere equations of elliptic type, Groningen, Noordhoff 1964
  • Differential Geometry, Groningen, Noordhoff 1967
  • Lectures on the foundations of geometry, Noordhoff 1966
  • Shells of positive Gaussian curvature under post- critical conditions, Jerusalem, Israel Program for Scientific Translations
  • Bendings of surfaces and stability of shells, American Mathematical Society 1988
Korocha Monge–Ampère equation Hilbert's problems Integrated Authority File
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