On Gromov's rigidity theorem for polytopes with acute angles
Differential Geometry
2025-07-08 v2
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.
Cite
@article{arxiv.2308.08000,
title = {On Gromov's rigidity theorem for polytopes with acute angles},
author = {S. Brendle and Y. Wang},
journal= {arXiv preprint arXiv:2308.08000},
year = {2025}
}
Comments
Minor changes to improve exposition, to appear in J. Reine Angew. Math