Efimov, Nikolai Vladimirovich

N.V. Efimov was born on May 18 ( 31 ), 1910 in Orenburg . In 1932 he graduated from North Caucasus State University (now Southern Federal University ). In 1934-1941 He worked at the University of Voronezh (since 1940 - professor), in 1941-1943. - at the Voronezh Aviation Institute ^[1] .

Since 1934, he has been a candidate of physical and mathematical sciences (the topic of the dissertation is “Bending surfaces with parabolic points” ), and since 1940, he has been a doctor of physical and mathematical sciences (the theme of the dissertation is “Invariant characteristics of some networks and surfaces” ). In 1946-1956 - Professor, Department of Mathematics, Faculty of Physics, Moscow State University ^[2] .

D 1943-1962 worked as head of the department of mathematics at the Moscow Forestry Institute ^[3] . Since 1946, he also taught at Moscow State University (MSU), which later became his main place of work ^[1] .

In 1957-1982 N.V. Efimov headed the Department of Mathematical Analysis of Mechanics and Mechanics of Moscow State University ^{[4] [5]} . In 1962-1969 he was dean of the Faculty of Mechanics and Mathematics of Moscow State University . In 1979, he was elected a corresponding member of the USSR Academy of Sciences ^[2] . He was a member of the editorial board of the "Mathematical Encyclopedia" .

Fields of scientific interests N. V. Efimova: differential geometry , applied mathematics ^[2] . Moreover, his main works relate to geometry and are devoted, in particular, to the theory of surface deformation and the theory of surfaces of negative curvature .

N.V. Efimov investigated the bending of a piece of surface near a flattening point and showed that there are analytic surfaces that are not flexible in any neighborhood of such a point. He solved the generalized Hilbert problem of surfaces having negative Gaussian curvature at all points. He generalized Hilbert’s theorem on immersion of the Lobachevsky plane , namely, he proved that on a complete regular surface in three-dimensional Euclidean space the Gaussian curvature is negative everywhere, then it has an exact upper bound equal to zero. In the theory of partial differential equations, he developed a method for studying nonlinear hyperbolic systems ^[6] .

Created and headed the Moscow school of geometers, engaged in the development of geometry issues "in general" ^[7] .

For his scientific achievements, N. V. Efimov was awarded a number of state awards and prizes ^[2] :

• Order of the Red Banner of Labor ( 1953 , 1971 );
• Lenin Prize ( 1966 ) - for research on the appearance of singularities on surfaces of negative curvature ;
• Prize named after N.I. Lobachevsky ( 1951 ).

Selected Editions

• Efimov N.V. Higher Geometry. - M.-L .: GITTL , 1945 .-- 485 p.
• Efimov N.V. Short course of analytic geometry. - M.-L .: GITTL , 1950 .-- 228 p.
• Efimov N.V. Quadratic forms and matrices. - M .: Fizmatgiz , 1962 .-- 160 p. - (Selected chapters of higher mathematics for engineers and students of technical schools).
• Efimov N.V., Rozendorn E.R. Linear algebra and multidimensional geometry. - M .: Nauka , 1970 .-- 528 p.
• Efimov N.V. Introduction to the theory of external forms. - M .: Nauka , 1977 .-- 88 p.

Some Articles

• Efimov N.V. Qualitative questions of the theory of surface deformations // Uspekhi Matematicheskikh Nauk . - 1948. - T. 3, no. 2 (24) . - S. 47-158 .
• Efimov N.V. Qualitative questions of the theory of surface deformations "in the small" // Transactions of Steklov Mathematical Institute of the USSR. - 1949.- T. 30 . - S. 3—128 .
• Efimov N.V. Surfaces with slowly varying negative curvature // Uspekhi Matematicheskikh Nauk . - 1966. - T. 21, no. 5 (131) . - S. 3-58 .

• Bogolyubov A.N. Mathematics. The mechanics. Biographical reference. - Kiev: Naukova Dumka , 1983 .-- 639 p.

• Mathematical Encyclopedic Dictionary, M.: Soviet Encyclopedia, 1988.
• A. D. Alexandrov, S. P. Novikov, A. V. Pogorelov, E. G. Poznyak, P. K. Rashevsky, E. R. Rozendorn, I. Kh. Sabitov, S. B. Stechkin . Nikolai Vladimirovich Efimov (obituary). UMN, 38: 5 (233) (1983), 111–117
• A. D. Alexandrov, Yu. A. Aminov, O. A. Oleinik, A. V. Pogorelov, E. G. Poznyak, E. R. Rozendorn, I. Kh. Sabitov . Nikolai Vladimirovich Efimov (on his seventieth birthday). UMN, 36: 3 (219) (1981), 233–238
• International conference "Metric geometry of surfaces and polyhedra" dedicated to the 100th birthday of Nikolai Vladimirovich Efimov
• We recall Nikolai Vladimirovich Efimov - ICMMO, 2014, 128 pages ISBN 978-5-4439-0134-3 , shooting gallery. 700 copies