Universal volume bounds in Riemannian manifolds
By Christopher Croke, Mikhail G. Katz. 2003
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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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1230bd45a6379ee8391ed5fb3939a63d3e08418b
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Entropy of systolically extremal surfaces and asymptotic bounds (2004, background): “See [ CK03 ] for a recent account on systolic inequalities.”