Lazar Aronovich Lyusternik (also Lusternik, Lusternick, Ljusternik; ; 31 December 1899 – 22 July 1981) was a Soviet mathematician. He is famous for his work in

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

and

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

, to which he applied the

variational principle A variational principle is a mathematical procedure that renders a physical problem solvable by the calculus of variations, which concerns finding functions that optimize the values of quantities that depend on those functions. For example, the pr ...

. Using the theory he introduced, together with Lev Schnirelmann, he proved the

theorem of the three geodesics In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical ...

, a conjecture by

Henri Poincaré Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philosophy of science, philosopher of science. He is often described as a polymath, and in mathemati ...

that every convex body in 3-dimensions has at least three simple

closed geodesic In differential geometry and dynamical systems, a closed geodesic on a Riemannian manifold is a geodesic that returns to its starting point with the same tangent direction. It may be formalized as the projection of a closed orbit of the geodesic f ...

s. The

ellipsoid An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a Surface (mathemat ...

with distinct but nearly equal axis is the critical case with exactly three closed geodesics. The ''Lusternik–Schnirelmann theory'', as it is called now, is based on the previous work by Poincaré, David Birkhoff, and

Marston Morse Harold Calvin Marston Morse (March 24, 1892 – June 22, 1977) was an American mathematician best known for his work on the ''calculus of variations in the large'', a subject where he introduced the technique of differential topology now known a ...

. It has led to numerous advances in differential geometry and topology. For this work Lyusternik received the Stalin Prize in 1946. In addition to serving as a professor of mathematics at Moscow State University, Lyusternik also worked at the Steklov Mathematical Institute (RAS) from 1934 to 1948 and the Lebedev Institute of Precise Mechanics and Computer Engineering (IPMCE) from 1948 to 1955. He was a student of

Nikolai Luzin Nikolai Nikolayevich Luzin (also spelled Lusin; rus, Никола́й Никола́евич Лу́зин, p=nʲɪkɐˈlaj nʲɪkɐˈlajɪvʲɪtɕ ˈluzʲɪn, a=Ru-Nikilai Nikilayevich Luzin.ogg; 9 December 1883 – 28 February 1950) was a Sov ...

. In 1930 he became one of the initiators of the Egorov affair and then one of the participants in the notorious political persecution of his teacher Nikolai Luzin known as the Luzin affair.

References

Pavel Alexandrov Pavel Sergeyevich Alexandrov (), sometimes romanized ''Paul Alexandroff'' (7 May 1896 – 16 November 1982), was a Soviet mathematician. He wrote roughly three hundred papers, making important contributions to set theory and topology. In topol ...

et al., LAZAR' ARONOVICH LYUSTERNIK (on the occasion of his 60th birthday), Russ. Math. Surv. 15 (1960), 153–168. * Pavel Alexandrov, In memory of Lazar Aronovich Lyusternik, Russ. Math. Surv. 37 (1982), 145-147

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* 1899 births 1981 deaths 20th-century Polish Jews 20th-century Polish mathematicians 20th-century Russian mathematicians People from Zduńska Wola People from Kalisz Governorate Academic staff of Moscow State University Corresponding Members of the USSR Academy of Sciences Moscow State University alumni Recipients of the Order of the Badge of Honour Recipients of the Order of Lenin Recipients of the Order of the Red Banner of Labour Recipients of the Stalin Prize Differential geometers Topologists Soviet mathematicians Burials at Kuntsevo Cemetery {{Russia-mathematician-stub

See also

References

External links