Sharp upper diameter bounds for compact shrinking Ricci solitons
Differential Geometry
2021-02-23 v2
Abstract
We give a sharp upper diameter bound for a compact shrinking Ricci soliton in terms of its scalar curvature integral and the Perelman's entropy functional. The sharp cases could occur at round spheres. The proof mainly relies on a sharp logarithmic Sobolev inequality of gradient shrinking Ricci solitons and a Vitali-type covering argument.
Keywords
Cite
@article{arxiv.2008.02893,
title = {Sharp upper diameter bounds for compact shrinking Ricci solitons},
author = {Jia-Yong Wu},
journal= {arXiv preprint arXiv:2008.02893},
year = {2021}
}
Comments
13 pages, coefficient of Theorem 1.1 improved, accepted by AGAG