Universal volume bounds in Riemannian manifolds
Differential Geometry
2007-05-23 v1 Geometric Topology
History and Overview
Abstract
In this survey article we will consider universal lower bounds on the volume of a Riemannian manifold, given in terms of the volume of lower dimensional objects (primarily the lengths of geodesics). By `universal' we mean without curvature assumptions. The restriction to results with no (or only minimal) curvature assumptions, although somewhat arbitrary, allows the survey to be reasonably short. Although, even in this limited case the authors have left out many interesting results.
Cite
@article{arxiv.math/0302248,
title = {Universal volume bounds in Riemannian manifolds},
author = {Christopher B. Croke and Mikhail G. Katz},
journal= {arXiv preprint arXiv:math/0302248},
year = {2007}
}
Comments
34 pages. To appear in Surveys in Differential Geometry