Integral curvature bounds, distance estimates and applications. (English) Zbl 0969.53017

Petersen, Peter; Sprouse, Chadwick

J. Differ. Geom. 50, No. 2, 269-298 (1998).

Authors’ summary: 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. Lévy isoperimetric constant to this situation. This gives generalizations of work of Lichnerowicz, Cheng, Croke, Gallot, Colding and more.

MSC:

53C20	Global Riemannian geometry, including pinching
53C65	Integral geometry

Keywords:

distance bound; mean curvature comparison; volume comparison; diameter bound; positive Ricci curvature; integral curvature bounds; isoperimetric constant