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arXiv · 2406.03284

Geometric inequalities for quasi-Einstein manifolds

Rafael Diógenes·Jaciane Gonçalves·Ernani Ribeiro Jr
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Abstract

In this article, we investigate certain geometric inequalities on quasi-Einstein manifolds. We use the generalized Reilly's formulas by Qiu-Xia and Li-Xia to establish new boundary estimates and an isoperimetric type inequality for compact quasi-Einstein manifolds with boundary. Boundary estimates in terms of the first eigenvalue of the Jacobi operator and the Hawking mass are also established. In particular, we present a Heintze-Karcher type inequality for compact domains in quasi-Einstein manifolds.

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Rafael Diógenes, Jaciane Gonçalves, Ernani Ribeiro Jr. 2024-06-05. Geometric inequalities for quasi-Einstein manifolds. https://arxiv.org/abs/2406.03284

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