On Gromov's rigidity theorem for polytopes with acute angles

S. Brendle; Y. Wang

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arXiv · 2308.08000

On Gromov's rigidity theorem for polytopes with acute angles

S. Brendle·Y. Wang

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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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S. Brendle, Y. Wang. 2023-08-15. On Gromov's rigidity theorem for polytopes with acute angles. https://arxiv.org/abs/2308.08000

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