Jeff Cheeger

Jeff Cheeger ( born December 1, 1943 in Brooklyn ) is an American mathematician who deals with differential geometry.

Cheeger studied at Harvard University ( BA 1964) and Princeton University, where he in 1966 made ​​his master's degree and received his doctorate at Salomon Bochner, 1967 ( Comparison and finite Ness theorems for Riemannian manifolds ). 1966/67, he was an assistant at Princeton and in 1968/69 Assistant Professor at the University of Michigan. 1969 and 1971 he was an associate professor at the State University of New York at Stony Brook with Detlef Gromoll. From 1971 he was a professor there until 1992. Since 1989 he is professor at the Courant Institute of Mathematical Sciences of New York University, from 2003 as a " Silver Professor ". He has been a visiting professor and visiting scientist at the IHES (1984 /85), at the MSRI (1985 ), Harvard (1972 ), in Rio de Janeiro ( at IMPA 1971) and the Institute for Advanced Study (1972, 1977, 1978, 1995 ).

Cheeger is known for various theorems in Riemannian geometry, such as the Soul theorem with Detlef Gromoll (for non - compact Riemannian manifolds with positive sectional curvature ) and the splitting theorem of Gromoll ( stating that a complete Riemannian manifold with non- negative Ricci curvature, which contains a " straight line", is isometric to the product, with L a manifold with positive Ricci curvature ) ..

In 1984 he was Guggenheim Fellow. He was invited speaker at the ICM 1974 ( Invariants of flat bundles ) and 1986 ( On the formulas of Atiyah - Patodi - Singer and Witten). He is a member of the National Academy of Sciences (1997) and the Finnish Academy of Sciences. In 1991 he received the Max Planck Research Prize together with Werner Müller. In 2001 he was awarded the Oswald Veblen - Prize of the American Mathematical Society, of which he is a Fellow.

Writings

• With David Ebin: Comparison theorems in Riemannian Geometry, 1975, AMS 2008
• A lower bound for the smallest eigenvalue of the Laplacian. Problems in analysis ( Papers dedicated to Salomon Bochner, 1969), pp. 195-199. Princeton Univ. Press, Princeton, N. J., 1970.
• With D. Gromoll: The splitting theorem for manifolds of Nonnegative Ricci curvature. J. Differential Geometry 6 (1971 /72), 119-128.
• With D. Gromoll: On the structure of complete manifolds of Nonnegative curvature. Ann. of Math ( 2) 96 (1972 ), 413-443.
• Analytic torsion and the heat equation. Ann. of Math ( 2) 109 (1979 ), no 2, 259-322.
• M. Gromov, M. Taylor: Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds. J. Differential Geom 17 (1982 ), no 1, 15-53.
• Spectral geometry of singular Riemannian spaces. J. Differential Geom 18 (1983 ), no 4, 575-657 (1984).
• With J. Simons: Differential characters and geometric invariants. Geometry and topology (College Park, Md., 1983/84 ), 50-80, Lecture Notes in Math, 1167, Springer, Berlin, 1985.
• With M. Gromov: L2 - cohomology and group cohomology. Topology 25 (1986 ), no 2, 189-215.
• With J.-M. Bismuth: - invariants and Their adiabatic limits. J. Amer. Math Soc. 2 (1989 ), no 1, 33-70.
• With T. Colding: On Lower bounds on Ricci curvature and the almost rigidity of warped products. Ann. of Math ( 2) 144 (1996 ), no 1, 189-237.
• With T. Colding: On the structure of spaces with Ricci curvature bounded below. I: J. Differential Geom 46 (1997 ), no 3, 406-480, . II: ibid. 54 (2000 ), no 1, 13-35; III: ibid. 54 (2000 ), no 1, 37-74.
• Differentiability of Lipschitz functions on metric measure spaces. Geom Funct. Anal. 9 (1999 ), no 3, 428-517.
• With B. Kleiner: Differentiating maps into, and the geometry of BV functions. Ann. of Math ( 2) 171 (2010 ), no 2, 1347-1385.