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Research Article | Open Access

Some almost-Schur type inequalities and applications on sub-static manifolds

School of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, China
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Abstract

In this paper, we establish some almost-Schur type inequalities on sub-static manifolds, naturally arising in General Relativity. In particular, our results generalize those in [1] of Li-Xia for r-th mean curvatures of closed sub-static hypersurfaces in space forms and k-scalar curvatures for closed locally conformally flat sub-static manifolds. Moreover, our results also generalize those of Cheng [2].

Keywords

almost-Schur type inequalitiessub-static manifoldsmean curvatureRicci curvature

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Electronic Research Archive
Volume 30 Issue 8,
August 2022
Pages 2860-2870
DOI: 10.3934/era.2022145

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Cite this article:
Zeng F. Some almost-Schur type inequalities and applications on sub-static manifolds. Electronic Research Archive, 2022, 30(8): 2860-2870. https://doi.org/10.3934/era.2022145

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Received: 27 June 2021
Revised: 07 April 2022
Accepted: 07 April 2022
Published: 15 August 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)