Lazar Lyusternik
Encyclopedia
Zdunska Wola
Zduńska Wola is a town in central Poland with 44,671 inhabitants .Situated in the Łódź Voivodeship , previously in Sieradz Voivodeship . It is the seat of Zduńska Wola County.- Famous people from Zduńska Wola :...
, Russian Empire
Russian Empire
The Russian Empire was a state that existed from 1721 until the Russian Revolution of 1917. It was the successor to the Tsardom of Russia and the predecessor of the Soviet Union...
– July 23, 1981 in Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
) was a Soviet mathematician.
He is famous for his work in topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
and differential geometry, to which he applied the variational principle
Variational principle
A variational principle is a scientific principle used within the calculus of variations, which develops general methods for finding functions which minimize or maximize the value of quantities that depend upon those functions...
. The theory he introduced, together
with Lev Schnirelmann
Lev Schnirelmann
Lev Genrikhovich Schnirelmann , also Shnirelman, Shnirel'man was a Soviet mathematician who sought to prove Goldbach's conjecture...
, proved a conjecture by Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
that every convex body in 3-dimensions has at least three closed geodesic
Geodesic
In mathematics, a geodesic is a generalization of the notion of a "straight line" to "curved spaces". In the presence of a Riemannian metric, geodesics are defined to be the shortest path between points in the space...
s. 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
George David Birkhoff
-External links:* − from National Academies Press, by Oswald Veblen....
, and Marston Morse
Marston Morse
Harold Calvin Marston Morse 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 as Morse theory...
. It has led to numerous advances in differential geometry and topology.
For this work Lyusternik received Stalin Prize
USSR State Prize
The USSR State Prize was the Soviet Union's state honour. It was established on September 9, 1966. After the breakup of the Soviet Union, the prize was followed up by the State Prize of the Russian Federation....
in 1946.
He was a student of Nikolai Luzin
Nikolai Luzin
Nikolai Nikolaevich Luzin, , was a Soviet/Russian mathematician known for his work in descriptive set theory and aspects of mathematical analysis with strong connections to point-set topology. He was the eponym of Luzitania, a loose group of young Moscow mathematicians of the first half of the...
. In 1930 he became one of the initiators of the Egorov affair
Dmitri Egorov
- External links :...
and then one of the participants in the notorious political persecution of his teacher Nikolai Luzin
Nikolai Luzin
Nikolai Nikolaevich Luzin, , was a Soviet/Russian mathematician known for his work in descriptive set theory and aspects of mathematical analysis with strong connections to point-set topology. He was the eponym of Luzitania, a loose group of young Moscow mathematicians of the first half of the...
known as the Luzin case or Luzin affair.
See also
- Lyusternik-Schnirelmann category
- Lyusternik's generalization of the Brunn-Minkowski theoremBrunn-Minkowski theoremIn mathematics, the Brunn–Minkowski theorem is an inequality relating the volumes of compact subsets of Euclidean space. The original version of the Brunn–Minkowski theorem applied to convex sets; the generalization to compact nonconvex sets stated here is due to L.A...