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Title:
Dihedral rigidity conjecture and Stoker's problem
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Abstract:
The Stoker Conjecture states that the dihedral angles of a convex Euclidean polyhedron completely determine the angles of each face. In this talk, I will present my recent work joint with Zhizhang Xie and Guoliang Yu that answers positively to the Stoker Conjecture in all dimensions. Our work proves a more general dihedral rigidity theorem, which concerns the comparison of scalar curvature, mean curvature, and dihedral angles for convex polyhedrons, or more general, manifolds with polytope boundary. We use index theory on manifolds with polytope boundary and the Dirac operator methods.
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