Lazar Aronovich Lyusternik (also Lusternik, Lusternick, Ljusternik; ; 31 December 1899, in

Zduńska Wola Zduńska Wola is a city in central Poland with 40,730 inhabitants (2021). It is the seat of Zduńska Wola County in the Łódź Voivodeship. The city was once one of the largest cloth, linen and cotton weaving centres in Poland and is the birthp ...

Congress Poland Congress Poland, Congress Kingdom of Poland, or Russian Poland, formally known as the Kingdom of Poland, was a polity created in 1815 by the Congress of Vienna as a semi-autonomous Polish state, a successor to Napoleon's Duchy of Warsaw. It w ...

Russian Empire The Russian Empire was an empire and the final period of the Russian monarchy from 1721 to 1917, ruling across large parts of Eurasia. It succeeded the Tsardom of Russia following the Treaty of Nystad, which ended the Great Northern War. ...

– 23 July 1981, in Moscow,

Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national ...

) was a

Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

mathematician. He is famous for his work in

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

and

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

, to which he applied the

variational principle In science and especially in mathematical studies, a variational principle is one that enables a problem to be solved using calculus of variations, which concerns finding functions that optimize the values of quantities that depend on those func ...

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

theorem of the three geodesics In differential geometry the theorem of the three geodesics, also known as Lyusternik–Schnirelmann theorem, states that every Riemannian manifold with the topology of a sphere has at least three simple closed geodesics (i.e. three embedded geode ...

, a conjecture by

Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...

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 flo ...

s. The

ellipsoid An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a surface that may be defined as the ...

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 Stalin Prize may refer to: * The State Stalin Prize in science and engineering and in arts, awarded 1941 to 1954, later known as the USSR State Prize The USSR State Prize (russian: links=no, Государственная премия СССР, ...

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 Nikolaevich Luzin (also spelled Lusin; rus, Никола́й Никола́евич Лу́зин, p=nʲɪkɐˈlaj nʲɪkɐˈlaɪvʲɪtɕ ˈluzʲɪn, a=Ru-Nikilai Nikilayevich Luzin.ogg; 9 December 1883 – 28 January 1950) was a Soviet/Ru ...

. 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

known as the Luzin case or Luzin affair.

References

Pavel Aleksandrov Pavel Sergeyevich Alexandrov (russian: Па́вел Серге́евич Алекса́ндров), sometimes romanized ''Paul Alexandroff'' (7 May 1896 – 16 November 1982), was a Soviet mathematician. He wrote about three hundred papers, ma ...

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

External links

* 1899 births 1981 deaths 20th-century Russian mathematicians Soviet mathematicians Moscow State University alumni Moscow State University faculty Differential geometers Topologists Stalin Prize winners 19th-century Polish Jews People from Zduńska Wola {{Russia-mathematician-stub

See also

References

External links