He worked as a teaching assistant and research assistant at Princeton University from 1966–1967, a National Science Foundation postdoctoral fellow and instructor from 1967–1968, an assistant professor from 1968 to 1969 at the University of Michigan, and an associate professor from 1969–1971 at SUNY at Stony Brook. Cheeger was a professor at SUNY, Stony Brook from 1971 to 1985, a leading professor from 1985 to 1990, and a distinguished professor from 1990 until 1992.
He has supervised at least 13 doctoral theses and three postdoctoral fellows. He has served as a member of several American Mathematical Society committees and National Science Foundation panels.
Cheeger has discovered many of the deepest results in Riemannian geometry, such as estimates for the spectrum of the Laplace-Beltrami operator, and the identity of the analytic and geometric definitions of torsion, and has led to the solution of problems in topology, graph theory, number theory, and Markov processes.[4]
Cheeger, Jeff; Kleiner, Bruce. On the differentiability of Lipschitz maps from metric measure spaces to Banach spaces. Inspired by S. S. Chern, 129–152, Nankai Tracts kn Mathematics. 11, World Science Publications, Hackensack, N.J., 2006.
Differentiability of Lipschitz functions on metric measure spaces. Geometric and Functional Analysis. 9 (1999), no. 3, 428–517.
Lower bounds on Ricci curvature and the almost rigidity of warped products, with T. H. Colding. Annals of Mathematics. 144. 1996. 189–237.
On the cone structure at infinity of Ricci flat manifolds with Euclidean volume growth and quadratic curvature decay, with Gang Tian. Inventiones Mathematicae. 118. 1994. 493–571.
Eta-invariants and their adiabatic limits, with J. M. Bismut. Journal of American Mathematical Society, 2, 1. 1989. 33–70.
Cheeger, Jeff; Gromov, Mikhail; Taylor, Michael Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds. Journal of Differential Geometry. 17 (1982), no. 1, 15–53.
On the Hodge theory of Riemannian pseudomanifolds. American Mathematical Society: Proceedings of the Symposium in Pure Mathematics. 36. 1980. 91–146. L² cohomology
Cheeger, Jeff; Gromoll, Detlef. The splitting theorem for manifolds of nonnegative Ricci curvature. Journal of Differential Geometry. 6 (1971/72), 119–128. Splitting theorem
A lower bound for the smallest eigenvalue of the Laplacian. Problems in analysis (Papers dedicated to Salomon Bochner, 1969), pp. 195–199. Princeton University Press, Princeton, N.J., 1970. Cheeger constant
Cheeger, Jeff; Gromoll, Detlef. The structure of complete manifolds of nonnegative curvature. Bulletin of the American Mathematical Society. 74 1968 1147–1150. Soul theorem
Cheeger, Jeff. Finiteness theorems for Riemannian manifolds. American Journal of Mathematics. 92 (1970) 61–74.
Cheeger, Jeff; Ebin, David G. Comparison theorems in Riemannian geometry. Revised reprint of the 1975[8] original. AMS Chelsea Publishing, Providence, RI, 2008.[9]
