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arXiv · 2009.12725

Geometric inequalities and rigidity of gradient shrinking Ricci solitons

Jia-Yong Wu
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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.

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Jia-Yong Wu. 2020-09-27. Geometric inequalities and rigidity of gradient shrinking Ricci solitons. https://doi.org/10.4310/ajm.250116215812

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