A note on scalar curvature and the convexity of boundaries

2012/09/20 by Martín Reiris, Martin Reiris, Reiris, Martin
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Boundary (topology) #Convexity #Curvature #Differential Geometry (math.DG) #FOS: Mathematics #Geodesic #Geometric Analysis and Curvature Flows #Geometry #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Prescribed scalar curvature problem #Pure mathematics #Regular polygon #Scalar (mathematics) #Scalar curvature #Sectional curvature #math.DG

paper · pdf · doi:10.48550/arxiv.1209.4525

arxiv created 2012/09/20 · openalex publication_date 2012/09/20 · arxiv updated 2012/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that any smooth Riemannian manifold of non-negative scalar curvature and with a strictly mean convex and compact boundary component can be (C²) extended beyond the component to have non-negative scalar curvature and to enjoy anyone of the following three types of (new) boundary: strictly convex, totally geodesic or strictly concave. The extension procedure can be applied for instance to "positive mass" type of theorems.

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