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Lazar Aronovich Lyusternik (December 31, 1899 in Zduńska Wola, Russian Empire – July 23, 1981 in Moscow) was a Soviet mathematician. He is famous for his work in topology and differential geometry, to which he applied the variational principle. The theory he introduced, together with Lev Schnirelmann, proved a conjecture by Henri Poincaré that every convex body in 3-dimensions has at least three closed geodesics. The ellipsoid with distinct but nearly equal axis is the critical case with exactly three closed geodesics.

The Lyusternik-Schnirelmann theory, as it is called now, is based on the previous work by Poincaré, David Birkhoff, and Marston Morse. It has led to numerous advances in differential geometry and topology. For this work Lyusternik received Stalin Prize in 1946.

He was a student of Nikolai Luzin. 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 case or Luzin affair.