descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 May 2016Embargo end date: 01 Jan 2014Publisher:International Press of BostonJournal:Journal of Differential Geometry, volume 103 (issn: 0022-040X,

Authors: Miao, Pengzi; Wang, Xiaodong;

doi: 10.4310/jdg/1460463563 , 10.48550/arxiv.1408.2711

arXiv: 1408.2711

Boundary effect of Ricci curvature

- Summary
- Subjects
- Metrics

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.

Related Organizations

Miami University
United States
Michigan State University
United States

Keywords

Mathematics - Differential Geometry, Differential Geometry (math.DG), FOS: Mathematics

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	9
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average