Jerry Kazdan

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

Life

Kazdan graduated from Rensselaer Polytechnic Institute with a bachelor 's degree in 1959 and the New York University with a master's degree in 1961 and his 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 Benjamin Peirce Instructor at Harvard University. In 1966 he was appointed Assistant Professor in 1974 and Professor at the University of Pennsylvania. From 1989 to 1992 he was faced with the mathematics faculty.

From 1974 to 1976 he was a visiting professor at the University of California, Berkeley, in 1981 at the University of Paris and 1971/72 at Harvard University. His doctoral counts Dennis Deturck.

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

Work

He is known for an inequality with Marcel Berger ( Berger- Kazdan comparison theorem ). He provides a lower bound for the volume of a compact n-dimensional Riemannian manifold with a given Injektivitätsradius:

Wherein the volume of the n-dimensional sphere with the radius R and the sign of equality is valid if and only if the manifold is isometric to the n- sphere. Thus, they also demonstrated along with Alan Weinstein conjecture by Wilhelm Blaschke on Reunion manifolds ( for straight dimensions), ie such oriented manifolds with the property that each point to a reunion pair ( x, y ) is one for which each geodesic passing through x by y and vice versa. Blaschke suspected that the Euclidean n- sphere is the only such variety in each dimension. Chung- Tao Yang proved in 1980 in the case of odd dimension.

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 exactly as scalar curvature, if it is negative somewhere on the manifold.

Writings

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