Boundary effect of Ricci curvature

Pengzi Miao, Xiaodong Wang

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)59-82
Number of pages24
JournalJournal of Differential Geometry
Volume103
Issue number1
StatePublished - May 1 2016

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Boundary Effect
Manifolds with Boundary
Ricci Curvature
Rigidity
Geometric Inequalities
Total curvature
Integral Inequality
Mean Curvature
Compact Manifold
Riemannian Manifold
Interior

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Geometry and Topology

Cite this

Boundary effect of Ricci curvature. / Miao, Pengzi; Wang, Xiaodong.

In: Journal of Differential Geometry, Vol. 103, No. 1, 01.05.2016, p. 59-82.

Research output: Contribution to journalArticle

Miao, P & Wang, X 2016, 'Boundary effect of Ricci curvature', Journal of Differential Geometry, vol. 103, no. 1, pp. 59-82.
Miao, Pengzi ; Wang, Xiaodong. / Boundary effect of Ricci curvature. In: Journal of Differential Geometry. 2016 ; Vol. 103, No. 1. pp. 59-82.
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