Geometric inequalities and rigidity of gradient shrinking Ricci solitons
Differential Geometry
2025-01-20 v2 Analysis of PDEs
Abstract
In this paper we prove that the Sobolev inequality, the logarithmic Sobolev inequality, the Schr\"odinger heat kernel upper bound, the Faber-Krahn inequality, the Nash inequality and the Rozenblum-Cwikel-Lieb inequality all equivalently exist on complete gradient shrinking Ricci solitons. We also obtain some integral gap theorems for compact shrinking Ricci solitons.
Keywords
Cite
@article{arxiv.2009.12725,
title = {Geometric inequalities and rigidity of gradient shrinking Ricci solitons},
author = {Jia-Yong Wu},
journal= {arXiv preprint arXiv:2009.12725},
year = {2025}
}
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