| Aleksey Vasilyevich Pogorelov
(on the occasion
of the 80th birthday)
||On the 3 May 1999 the
prominent scientist and wonderful person, a Member of Academy of Sciences of Russia and
National Academy of Sciences of Ukraine, an honorary member of Moscow Mathematical Society
Aleksey Vasilyevich Pogorelov was 80 years old.
A.V. Pogorelov was born in Korocha town (Belgorod
region). He received his education at Kharkov State University (KSU, 1937-1941) and Air
Force Academy named after N.E. Zhukovsky (Moscow, 1941-1945). Since 1945 he was working
года работал в ЦАГИ and at the same time taking his post graduate course
in "geometry and topology" at Moscow State University. A.V.'s tutors were well
known mathematicians and teachers, the creators of the national science school of geometry
"in general" proffesors N.V. Yefimov A.D. Aleksandrov. He was awarded M.Sc., and
in another year Doctor of Science. After that he returned to Kharkov (1947) where he soon
became head of the chair of geometry in KSU. In 1960 A.V. began working in ILTPE
(Institute of Low Temperature Physics & Engineering) where he has been up until now
heading the geometry section in the Mathemathics Department. In 1951 A.V. was elected a
Corresponding Member, and in 1960 a full member of the Academy of Sciences of Ukraine, as
of this same year he is a Corresponding Member, and since 1976 - a full member the Academy
of Sciences of Soviet Union.
Brilliant mathematical gift and outstanding engineering
talent determined the wide range of A.V. Pogorelov's scientific interests, that involves
both fundamental and applied fields. He gets the credit for resolving a number of key
problems in "general" geometry, in basic geometry, in Monge-Ampere equation
theory as well as significant results in thin resilient shells stability geometrical
theory. The very first A.V.'s deep research into the difficult problem of exact
determination of common convex surfaces by their measure which had been first mentioned by
A.Cauchy, D.Hilbert and S.E.Con-Fossen made him one of the leading figures of the world
science. This scientific achievment triggered a qualitative improvement in the theory of
irregular surfaces, the elements of this theory had been established a long time before
that by A.D.Aleksandrov. It had determined the priorities of this theory for generations
Later on A.V.Pogorelov solved a number of other complex
problems of "general" geometry, in particular the problem of regularity of a
convex surface with regular metrics, the Weyl problem on convex metrics feasibility for
Riemann spaces, the problem of infinitely small curves of convex surfaces, the problem of
improper convex affined hyperspheres. He also accomplished a complete solution of the
fourth Hilbert problem and the regular solution of the multidimensional Minkovsky problem.
This works stimulated the creation of a new division of mathematical research -- the outer
geometry of convex surfaces, that became a logical conclusion and completion of
A.D.Aleksandrov's theory --inner geometry of convex surfaces. They established the theory
of convex surfaces as a division of classical differential geometry. He built the theory
of limited outer curvature surfaces (1956), worked out the general geometrical theory of
Monge-Ampere equations for three dimensional (1960) and multidimensional (1983) cases,
considerably extended G.Buseman theory of G-spaces (1998).
Just recently he has found a complete solution to
another very important problem as he has proved the equality of twice derivable closed
convex surfaces having positive Gauss curvature, for which the second differential of
support functions difference is either sign-changeable form or equal to zero. This theorem
for the case of analitical surfaces was established as early as in 1939 by
A.D.Aleksandrov. Numerous attempts to weaken the condition of analysis to the natural
level were unsuccessful up until 1999.
It should be pointed out here that in the process of research works A.V. Pogorelov
displayed himself to be not only a great geometry expert, but also a prominent analyst.
A. V. Pogorelov has developed a new original geometrical approach to solving the
problems of thin resilient shells stability, he conducted a number of high precision
experiments that proved his theory. He was one of the first researchers in the U.S.S.R.
(1970) to suggest the new idea of constructing of synchronized cryoturbogenerator with
superconductive exitation winding, which prompted the development of cryogenics mechanical
engineering in our country. Later A.V. Pogorelov took active part in theoretical
calculations and technical implementation of industrial models of cryoturbogenerators,
developed in ILTPE (Institute of Low Temperature Physics & Engineering).
A.V. Pogorelov wrote numerous monographs, manuals on basic subjects of geometry for
higher education institutions and the well known geometry school text book, which has been
adopted for use in schools since 1982. A.V.'s books are written in a clear and distinct
language. They wer reprinted many times and in many countries.
We can hardly find another mathematician, who enriched the science with as many
forceful, deep and useful results in geometry.
Aleksey Vasilyevich Pogorelov was awarded many rewards and honorary titles. He won the
international N.I. Lobachevsky prize, the Lenin prize, state prizes of Ukraine and the
U.S.S.R., personal awards of the National Science academy of Ukraine. A.V. is a
distinguished figure in science and owner of government awards.
We sincerely wish Aleksey Vasilyevich good health, happiness, the pleasure of new
||A.D. Aleksandrov, A.A. Borisenko,
V.A. Zalgaller, V.A. Marchenko, K.V. Maslov, A.D. Milka, S.P. Novikov, Y.G. Reshetnyak,
I.V. Skrypnik, Y.Y. Khruslov
index of published works by Aleksey Vasilyevich Pgorelov
бесконечно малые изгибания конических
поверхностей // ДАН СССР.- 1988.- Т. 303, N 3.
165. Потеря устойчивости
развертывающихся оболочек // ДАН СССР.-1989.- Т.304, N 5.
166. Потеря устойчивости
конических оболочек под внешним давлением // ДАН
СССР.- 1989.- Т. 309, N 4.
167. Потеря устойчивости
конических оболочек при кручении // ДАН СССР. - 1989.-
Т. 309, N 4.
168. Bending of surfaces and stability of shells //
Transl. of math. monographs, V.72. Amer. Math. Soc.
169. Об учебнике "Геометрия
7-11" // Математика в школе.- 1989.- N 5.
170. Геометрия (учебник для 7-11
классов общеобразовательных учреждений).- М.:
171. G-пространства Г. Буземана с
римановой метрикой // ДАН СССР.- 1990.- Т. 313, N 5.
172. Регулярные G-пространства Г.
Буземана // ДАН СССР.- 1990.- Т. 314, N 1.
173. Решение одной проблемы Г.
Буземана // ДАН СССР.- 1990.- Т. 314, N 4.
174. Об одной теореме Бельтрами
// ДАН СССР,- 1991.- Т. 316, N 2.
175. Потеря устойчивости
цилиндрических оболочек при неравномерном
осевом сжатии // ДАН СССР.- 1991.- Т. 318, N 6.
176. О нижнем пределе
критической нагрузки при осевом сжатии
цилиндрической оболочки // ДАН СССР.- 1992.- Т. 324, N 3.
177. Геометрические методы в
теории устойчивости оболочек (обзор) //
Прикладная механика.- 1992.- Т. 28, N 1.
178. Generalized solutions of Monge-Ampere equations of
elliptic type (review) // A Tribute to Ilya Bakelman, Discourses in Mathematics and its
Applications, N 3, Department of Mathematics, Texas A&M University, College Station,
Texas, 1994, pp.47-50.
179. Вложение "мыльного
пузыря" внутрь тетраэдра // Математические
заметки.- 1994.- Т. 56, вып. 2.
180. Потеря устойчивости общих
цилиндрических оболочек при осевом сжатии // ДАН
России. - 1994.- Т. 337, N 3.
181. Геометpiя, 7 - 9. - К.: Освiта, 1994.
182. Геометpiя, 10 - 11.- К.: Освiта, 1994.
183. Изгибание выпуклой
поверхности в выпуклую с заданным сферическим
изображением // Математические заметки.- 1995.- Т. 58,
184. Multidimensional Monge-Ampere equation // Harwood
Academic Publishers, Rev. in Math. and Math. Phys., 1995, v. 10.
185. Buseman regular G-spaces // Harwood Academic
Publishers, Rev. In Math. and Math. Phys., 1998, v. 10, part 4.
186. Исследование плоскости в
абсолютной геометрии // ДАН России.- 1996.- Т. 348, N 4.
187. Изгибание поверхностей и
устойчивость оболочек.- К.: Наукова думка, 1998.
188. Решение одной проблемы А.Д.
Александрова // ДАН России.- 1998.- Т. 360, N 3.
189. О теоремах единственности
для замкнутых выпуклых поверхностей // ДАН России
first part of the index is published in: Mathematics in the U.S.S.R. over a 40 year
period. 1917-1957 (М.: Физматгиз, 1959.- Т. 2.- С. 547-548), and also in:
Математика в СССР, 1958-1967 (М.: Наука, 1970.- Т. 2.- С.
1052-1053), УМН (1979.- Т.34, вып. 4(208).- С.225-226; 1989.- Т. 44, вып.
4(268).- С. 249).