A refinement of G\"unther's candle inequality
Differential Geometry
2013-07-19 v3
Abstract
We analyze an upper bound on the curvature of a Riemannian manifold, using "root-Ricci" curvature, which is in between a sectional curvature bound and a Ricci curvature bound. (A special case of root-Ricci curvature was previously discovered by Osserman and Sarnak for a different but related purpose.) We prove that our root-Ricci bound implies G\"unther's inequality on the candle function of a manifold, thus bringing that inequality closer in form to the complementary inequality due to Bishop.
Keywords
Cite
@article{arxiv.1204.3943,
title = {A refinement of G\"unther's candle inequality},
author = {Benoit Kloeckner and Greg Kuperberg},
journal= {arXiv preprint arXiv:1204.3943},
year = {2013}
}
Comments
v2: significant change of notation in root-Ricci curvature, references added in the entropy part, other minor corrections. v3: small corrections