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May 2016 Boundary effect of Ricci curvature
Pengzi Miao, Xiaodong Wang
J. Differential Geom. 103(1): 59-82 (May 2016). DOI: 10.4310/jdg/1460463563

Abstract

On a compact Riemannian manifold with boundary, we study how Ricci curvature of the interior affects the geometry of the boundary. First, we establish integral inequalities for functions defined solely on the boundary and apply them to obtain geometric inequalities involving the total mean curvature. Then, we discuss related rigidity questions and prove Ricci curvature rigidity results for manifolds with boundary.

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Pengzi Miao. Xiaodong Wang. "Boundary effect of Ricci curvature." J. Differential Geom. 103 (1) 59 - 82, May 2016. https://doi.org/10.4310/jdg/1460463563

Information

Published: May 2016
First available in Project Euclid: 12 April 2016

zbMATH: 1341.53064
MathSciNet: MR3488130
Digital Object Identifier: 10.4310/jdg/1460463563

Rights: Copyright © 2016 Lehigh University

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Vol.103 • No. 1 • May 2016
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