Appears in collection : Not Only Scalar Curvature Seminar

In this talk, I will review Gromov’s dihedral extremality and rigidity conjectures regarding comparisons of scalar curvature, mean curvature and dihedral angle for compact manifolds with corners. These conjectures have profound implications in geometry and mathematical physics such as the positive mass theorem. I will explain the recent work on positive solutions to these conjectures, and some related applications (such as a positive solution to the Stoker conjecture). The talk is based on my joint works with Jinmin Wang and Guoliang Yu.