Jerry Kazdan

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Jerry Kazdan (1974)

Jerry Lawrence Kazdan (born October 31, 1937 in Detroit , Michigan ) is an American mathematician who studies partial differential equations and differential geometry .

Life

Kazdan studied at the Rensselaer Polytechnic Institute with a bachelor's degree in 1959 and at New York University with a master's degree in 1961 and a doctorate in 1963 under Paul Garabedian ( A Boundary Value Problem Arising in the Theory of Univalent Functions ). at the Courant Institute . From 1963 to 1966 he was a Benjamin Peirce Instructor at Harvard University . In 1966 he became an assistant professor and in 1974 professor at the University of Pennsylvania . From 1989 to 1992 he headed the mathematics faculty.

From 1974 to 1976 he was visiting professor at the University of California, Berkeley , 1981 at the University of Paris and 1971/72 at Harvard University. Dennis DeTurck is one of his PhD students .

He was a member of the Arthur Besse collective . In 1999 he received the Lester Randolph Ford Award for Solving equations, an elegant legacy . He is a fellow of the American Mathematical Society .

plant

He is known for an inequality with Marcel Berger (Berger-Kazdan comparison theorem). It gives a lower bound for the volume of a compact n-dimensional Riemann manifold with a given injectivity radius :

where is the volume of the n-dimensional sphere with radius r and the equals sign applies if and only if the manifold is isometric to the n-sphere. With this they proved, together with Alan Weinstein, a conjecture by Wilhelm Blaschke about reunion manifolds (for even dimensions), that is, such oriented manifolds with the property that every point belongs to a reunion pair (x, y), for each Geodesic goes through x also through y and vice versa. Blaschke assumed that the Euclidean n-sphere is the only such manifold in every dimension. In 1980, Chung-Tao Yang proved the case of odd dimensions.

He also made significant contributions to the theory of Riemannian manifolds with prescribed scalar curvature with Frank W. Warner . Both proved in 1975 that any smooth function can be realized as a scalar curvature if and only if it becomes negative somewhere on the manifold.

Fonts

  • Prescribing the curvature of a Riemannian manifold, CBMS Regional Conference 1984, American Mathematical Society 1985

Web links

Individual evidence

  1. ↑ Life data according to American Men and Women of Science , Thomson Gale 2004
  2. ^ Mathematics Genealogy Project
  3. ↑ Amer. Math. Monthly 105 (1998) 1-21
  4. ^ Mathworld
  5. ↑ Berger, Kazdan A Sturm-Liouville inequality with applications to an isoperimetric inequality for volume in terms of injectivity radius, and to Wiedersehen manifolds , Proceedings of Second International Conference on General Inequalities, 1978, Birkhäuser 1980, pp. 367-377
  6. ↑ Kazdan, Warner Scalar curvature and conformal deformation of Riemannian structure , Journal of Differential Geometry, 10 (1975). 113-134
  7. ↑ Kazdan, Warner Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvature , Annals of Mathematics, Volume 101, 1975, pp. 317-331
personal data
SURNAME Kazdan, Jerry
ALTERNATIVE NAMES Kazdan, Jerry Lawrence (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH October 31, 1937
PLACE OF BIRTH Detroit , Michigan