Gromov's Rigidity Theorem for Polytopes with Acute Angles

Explore a 59-minute lecture on Gromov's rigidity theorem for polytopes with acute angles, presented by Yipeng Wang from Columbia University at the Institut des Hautes Etudes Scientifiques (IHES). Delve into Gromov's conjecture on the scalar curvature extremality property of convex polytopes and learn about S. Brendle's recent proof using Dirac operator techniques and a smoothing construction. Examine Gromov's outlined proof for cases with acute dihedral angles and discover recent developments in the dihedral rigidity problem. Gain insights into the joint work of S. Brendle and Y. Wang, which introduces an alternative smoothing construction for Gromov's argument. Understand how their proof of the rigidity statement relies on a deep estimate by Fefferman and Phong. Reference the arXiv paper "On Gromov's rigidity theorem for polytopes with acute angles" for further study.