Aleksei Pogorelov

In 2015, one of the streets in Kharkiv was named after Academician A.V. Pogorelov.

In 2007, National Academy of Sciences of Ukraine founded the Pogorelov Award for the achievements in the field of geometry and topology.

He died on December 17, 2002 and was buried in Moscow at the Nikolo-Arkhangelsk cemetery.

Since 2000 he lived in Moscow and worked at the Steklov Institute of Mathematics.

One of the asteroids is named after A.V. Pogorelov: (19919) Pogorelov [fr].

A. V. Pogorelov was one of the first who has proposed (in 1970) a new idea in the construction of a cryoturbogenerator with superconducting field winding and took an active part in technical calculations and creation of corresponding industrial samples.

The first work of A. V. Pogorelov on surfaces of bounded extrinsic curvature was published in 1953. In 1954, J. Nash published the paper on С-isometric immersions, which was improved by N. Kuiper in 1955. It follows from these studies that a Riemannian metric defined on a two-dimensional manifold, under very general assumptions, admits a realization on a С-smooth surface in a three-dimensional Euclidean space. Moreover, this realization is carried out as freely as a topological immersion into the space of the manifold on which the metric is given. Hence it is clear that for С-surfaces, even with a good intrinsic metric, it is impossible to preserve the connections between the intrinsic and extrinsic curvatures. Even in case if a С-surface carries a regular metric of positive Gaussian curvature, then this does not imply the local convexity of the surface. This emphasizes the naturalness of the class of surfaces of bounded external curvature introduced by A. V. Pogorelov.

The desire to complete university education and specialize in geometry professionally led A.V. Pogorelov to Moscow State University. By recommendation of I.G. Petrovsky (Dean of the Mechanics and Mathematics Department) and a well-known geometer V.F. Kagan, Aleksei Vasil'evich met A.D. Aleksandrov – the founder of the theory of non-smooth convex surfaces. There were many new questions concerning this theory. Aleksandr Danilovich proposed to give an answer to one of them to A.V. Pogorelov. In a year the problem was solved and A.V. Pogorelov was enrolled to the graduate school of the Mechanics and Mathematics Department of Moscow State University. Nikolai Efimov became his scientific advisor on topics of Aleksandrov theory. After defending his Ph.D. thesis in 1947, he was demobilized and moved to Kharkiv, where he started to work at the Institute of Mathematics of Kharkov State University and the Geometry Department of the university. In 1948 he defended his doctoral thesis. In 1951 he became the Corresponding Member of the Academy of Sciences of Ukraine, in 1960 he became the Corresponding member of the USSR Academy of Sciences (Division of Physical and Mathematical Sciences). In 1961 he became an Academician of the Academy of Sciences of Ukraine. In 1976, he became an Academician of the USSR Academy of Sciences (Mathematics Division). From 1950 to 1960 he was the Head of the Geometry Department at Kharkiv State University. From 1960 to 2000 he was the Head of the Geometry Division at the Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine.

In 1941, after the involvement of the Soviet Union in the World War II, Aleksei Vasil'evich was sent for 11 months study to N.Y. Zhukovsky Air Force Engineering Academy. During his studies, the students periodically were sent for several months to the front as technicians for the airplane service. After the Red Army Victory over Nazi near Moscow, the training continued for a full term. After academy graduation, he worked at N.Y. Zhukovsky Central Aero-hydrodynamic Institute (TsAGI) as a design engineer.

Aleksei Vasil'evich Pogorelov (Russian: Алексе́й Васи́льевич Погоре́лов, Ukrainian: Олексі́й Васи́льович Погорє́лов; March 2, 1919 – December 17, 2002), was a Soviet and Ukrainian mathematician. Specialist in the field of convex and differential geometry, geometric PDEs and elastic shells theory, the author of the novel school textbook on geometry and university textbooks on analytical geometry, on differential geometry, and on foundations of geometry.

Born March 3, 1919 in Korocha, Kursk Governorate (now Belgorod region) in a peasant family. In 1931, because of the collectivization, the parents of Pogorelov escaped from the village to Kharkiv, where his father become a worker at the construction of the Kharkiv tractor plant. In 1935, A.V. Pogorelov won the first prize at the Mathematical Olympiad in Kharkiv State University. After high school graduation in 1937, he entered the mathematical department of the Kharkiv State University. He was the best student at the department.

A. V. Pogorelov solved Hilbert's fourth problem, set by D. Hilbert at the II International Congress of Mathematicians in Paris in 1900. He found all, up to isomorphism, realizations of the systems of axioms of classical geometries (Euclid, Lobachevsky and elliptic) if one omits the congruence axioms containing the concept of angle and supplement these systems with the axiom of "triangle inequality".

For domains on convex surfaces assertions 1) and 2) are false. The local and global properties of surfaces are significantly different. By proving assertion 1) A.V. Pogorelov completed the solution of the problem open for more than a century. The first result in this direction was obtained by Cauchy for closed convex polyhedra in 1813.