Geometric inequalities for quasi-Einstein manifolds
Differential Geometry
2025-07-01 v2
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.
Cite
@article{arxiv.2406.03284,
title = {Geometric inequalities for quasi-Einstein manifolds},
author = {Rafael Diógenes and Jaciane Gonçalves and Ernani Ribeiro},
journal= {arXiv preprint arXiv:2406.03284},
year = {2025}
}
Comments
To appear in Annali di Matematica Pura ed Applicata