Three-manifolds of positive Ricci curvature and convex weakly umbilic boundary

2007/04/17 by Jean C. Cortissoz, Jean Cortissoz, Cortissoz, Jean · 1 citation
Mathematics · #37E35 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #math.DG #msc:37E35

paper · pdf · doi:10.48550/arxiv.0704.2081

14 pages

arxiv created 2007/04/17 · openalex publication_date 2007/04/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider three-manifolds with weakly umbilic boundary (the Second Fundamental form of the boundary is a constant multiple of the metric). We show that if the initial manifold has positive Ricci curvature and the boundary is convex (nonnegative Second Fundamental form), its metric can be deformed via the Ricci flow to a metric of constant curvature and totally geodesic boundary.

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