Jeff Cheeger

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Jeff Cheeger (left) with H. Blaine Lawson at IHES 2007

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

Life

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

Cheeger is known for various theorems in Riemannian geometry, for example the Soul theorem with Detlef Gromoll (for non-compact Riemannian manifolds with positive sectional curvature ) and the decomposition theorem with Gromoll (which says that a complete Riemannian manifold with non-negative Ricci -Curvature that contains a “straight line” is isometric to the product , with L being a manifold with non-negative Ricci curvature).

The set of Cheeger and Mueller (independent of Cheeger and Werner Müller proved) states the equivalence of analytical (Ray Singer) continuous torsion and Reidemeister torsion of compact Riemannian manifolds . They thus proved a conjecture by DB Ray and Isadore M. Singer .

In 1970 he received a research grant from the Alfred P. Sloan Foundation ( Sloan Research Fellowship ). In 1984 he was a Guggenheim Fellow. He was invited speaker at the ICM in 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 and Werner Müller received the Max Planck Research Award . In 2001 he received the Oswald Veblen Prize of the American Mathematical Society , of which he is a fellow. He has also been an elected member of the American Academy of Arts and Sciences since 2006 . For 2019, Cheeger was awarded the Leroy P. Steele Prize for his life's work .

Fonts

  • 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, NJ, 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: 413-443 (1972).
  • Analytic torsion and the heat equation. Ann. of Math. (2) 109 (1979) no. 2, 259-322.
  • with 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.

See also

Web links

Remarks

  1. ↑ See the article about Detlef Gromoll
  2. ↑ a geodetic line that minimizes the distance between any two points on it
  3. ↑ Cheeger, Gromoll: The splitting theorem for manifolds of non-negative Ricci curvature , Journal of Differential Geometry, Vol. 6, 1971/72, pp. 119-128
  4. ↑ Müller, Analytic torsion and R-torsion of Riemannian manifolds, Adv. In Math., Volume 28, 1978, pp. 233-305
  5. ↑ Jeff Cheeger, Analytic Torsion and Reidemeister Torsion, Proc. Nat. Acad. Sci. USA, Vol. 74, 1977, pp. 2651-2654
  6. ↑ Jeff Cheeger, Analytic torsion and the heat equation, Annals of Mathematics, Volume 109, 1979, pp. 259-322
personal data
SURNAME Cheeger, Jeff
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH December 1, 1943
PLACE OF BIRTH Brooklyn