A $(\log n)^{\Omega(1)}$ integrality gap for the Sparsest Cut SDP (2009)
Cheeger, Jeff, Kleiner, Bruce, Naor, Assaf
We show that the Goemans-Linial semidefinite relaxation of the Sparsest Cut problem with general demands has integrality gap $(\log n)^{\Omega(1)}$. This is achieved by exhibiting $n$-point metric...
Compression bounds for Lipschitz maps from the Heisenberg group to $L_1$ (2009)
Cheeger, Jeff, Kleiner, Bruce, Naor, Assaf
We prove a quantitative bi-Lipschitz nonembedding theorem for the Heisenberg group with its Carnot-Carath\'eodory metric and apply it to give a lower bound on the integrality gap of the...
Metric differentiation, monotonicity and maps to L^1 (2009)
We give a new approach to the infinitesimal structure of Lipschitz maps into L^1. As a first application, we give an alternative proof of the main theorem from an earlier paper, that the Heisenberg...
CHARACTERIZATION OF THE RADON-NIKODYM PROPERTY IN TERMS OF INVERSE LIMITS (2009)
Abstract. In this paper we clarify the relation between inverse systems, the Radon-Nikodym property, the Asymptotic Norming Property of James-Ho [JH81], and the GFDA spaces introduced in
We prove the differentiability of Lipschitz maps X-->V, where X is a complete metric measure space satisfying a doubling condition and a Poincar\'e inequality, and V is a Banach space with the Radon...
Abstract. This is one of a series of papers examining the interplay between differentiation theory for Lipschitz maps, X → V, and bi-Lipschitz nonembeddability, where X is a metric measure space...
denote the universal covering space of a compact Riemannian (2007)
Jianguo Cao, Jeff Cheeger, Xiaochun Rong
manifold, M
Characterization of the Radon-Nikodym Property in terms of inverse limits (2007)
We clarify the relation between inverse systems, the Radon-Nikodym property, the Asymptotic Norming Property of James-Ho, and the GFDA spaces introduced in our earlier paper on differentiability of...
Differentiating maps into L^1 and the geometry of BV functions (2006)
This is one of a series of papers examining the interplay between differentiation theory for Lipschitz maps, X-->V, and bi-Lipschitz nonembeddability, where X is a metric measure space and V is a...
On the differentiation of Lipschitz maps from metric measure spaces to Banach spaces (2006)
Abstract. We consider metric measure spaces satisfing a doubling condition and a Poincaré inequality in the upper gradient sense. We show that the results of [Che99] on differentiability of real...
Generalized differentiation and bi-Lipschitz nonembedding (2006)
Résumé. We consider Lipschitz mappings f: X → V, where X is a doubling metric measure space which satisfies a Poincaré inequality, and V is a Banach space. We show that earlier differentiability...
Local splitting structures on nonpositively curved manifolds and semirigidity in dimension 3 (2004)
Cao , Jianguo, Cheeger , Jeff, Rong , Xiaochun
Let Mn denote a closed Riemannian manifold with nonpositive sectional curvature. Let Xn denote a closed smooth manifold which admits an F- structure, \frak F. If there exists f : Xn → Mn with...
Splittings and Cr-structures for manifolds with nonpositive sectional curvature (2001)
Jianguo Cao, Jeff Cheeger, Xiaochun Rong
Let denote the universal covering space of a compact Riemannian , with sectional curvature, 0. We show that a collection of deck transformations of , satisfying certain (metric dependent) conditions,...
On the structure of spaces with Ricci curvature bounded below (1997)
Jeff Cheeger, Tobias H. Colding
In this paper and in [12], [13], we study the structure of spaces, Y, which are pointed Gromov-Hausdorff limits of sequences, f(M
Cheeger, Jeff, De Bartolomeis, Paolo, Tricerri, Franco
Incluye bibliografía
Comparison and finiteness theorems for Riemannian manifolds [microform] / (1967)
Thesis (Ph. D.)--Princeton University, 1967.
Comparison and finiteness theorems for Riemannian manifolds / (1967)
Thesis (Ph. D.)--Princeton University, 1967.
Comparison and finiteness theorems for Riemannian manifolds. (1967)
Thesis (Ph. D.)--Princeton.
On the spectral geometry of spaces with cone-like singularities
I describe an extension of a portion of the theory of the Laplace operator on compact riemannian manifolds to certain spaces with singularities. Although this approach can be extended to include...
Analytic torsion and Reidemeister torsion
We announce a proof of the conjecture of Ray and Singer that for a compact Riemannian manifold the analytic torsion and Reidemeister torsion are equal. The proof involves studying the heat equation...
On the spectral geometry of spaces with cone-like singularities
I describe an extension of a portion of the theory of the Laplace operator on compact riemannian manifolds to certain spaces with singularities. Although this approach can be extended to include...
Analytic torsion and Reidemeister torsion
We announce a proof of the conjecture of Ray and Singer that for a compact Riemannian manifold the analytic torsion and Reidemeister torsion are equal. The proof involves studying the heat equation...