Scalar curvature rigidity of geodesic balls in Sⁿ

2010/05/16 by Simon Brendle, Fernando C. Marques, Brendle, S. +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1005.2782

openalex publication_date 2010/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove a scalar curvature rigidity result for geodesic balls in Sⁿ. This result contrasts sharply with the recent counterexamples to Min-Oo's conjecture for the hemisphere (cf. [5]).

Citations

• On the proof of the positive mass conjecture in general relativity
• A new proof of the positive energy theorem

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