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On Gromov's rigidity theorem for polytopes with acute angles

2023/08/15 by Simon Brendle, Yanming Wang, Brendle, S. +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2308.08000

openalex publication_date 2023/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In his ``Four Lectures", Gromov conjectured a scalar curvature extremality property of convex polytopes. Moreover, Gromov outlined a proof of the conjecture in the special case when the dihedral angles are acute. Gromov's argument relies on Dirac operator techniques together with a smoothing construction. In this paper, we give the details of such a smoothing construction, thereby providing a detailed proof of Gromov's theorem.

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