Integral curvature bounds, distance estimates and applications

Peter Petersen, Chadwick Sprouse

Type: Article

Publication Date: 1998-01-01

Citations: 71

DOI: https://doi.org/10.4310/jdg/1214461171

Abstract

In this paper we show how the classical diameter bound for manifolds with positive Ricci curvature generalizes to a situation where one has integral curvature bounds.In addition we also generalize the P. Levy isoperimetric constant to this situation.This gives generalizations of work of Lichnerowicz, Cheng, Croke, Gallot, Colding and more.

Locations

Journal of Differential Geometry - View - PDF

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Works Cited by This (33)

Action	Title	Year	Authors
+ PDF Chat	A general comparison theorem with applications to volume estimates for submanifolds	1978	Ernst Heintze Hermann Karcher
+ PDF Chat	Three-manifolds with positive Ricci curvature	1982	Richard S. Hamilton
+ PDF Chat	Distance spheres and Myers-type theorems for manifolds with lower bounds on the Ricci curvature	1990	Yoe Itokawa
+ PDF Chat	Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds	1982	Jeff Cheeger M. Gromov Michael E. Taylor
+ PDF Chat	On the structure of spaces with Ricci curvature bounded below. I	1997	Jeff Cheeger Tobias Colding
+	On eigenvalue pinching in positive Ricci curvature	1999	Peter Petersen
+	Riemannian manifolds with positive mean curvature	1941	S. B. Myers
+	Riemannian manifolds with non-negative Ricci curvature	1972	André Avez
+	On the neighborhood of a geodesic in Riemannian space	1935	J. L. Synge
+	Relative Volume Comparison with Integral Curvature Bounds	1997	Peter Petersen Guofang Wei