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On Gromov's flat corner domination conjecture and Stoker's conjecture

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arxiv 2203.09511 v2 pith:TFRBQ5XX submitted 2022-03-17 math.DG math.KT

Jinmin Wang , Zhizhang Xie This is my paper · ORCID
classification math.DGmath.KT
keywords conjectureconvexcornerdimensionsdominationeuclideanflatgromov
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In this paper, we prove Gromov's flat corner domination conjecture in all dimensions. As a consequence, we answer positively the Stoker conjecture for convex Euclidean polyhedra in all dimensions. By applying the same techniques, we also prove a rigidity theorem for strictly convex domains in Euclidean spaces.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Dihedral Rigidity for Convex Polytopes by Smooth Approximation

    math.DG 2026-08 accept novelty 8.0 of 10

    Gromov's dihedral rigidity conjecture for convex polytopes is proved in all dimensions n≥3 using smooth inner approximations and Dirac operator estimates.

  2. A scalar-mean curvature comparison theorem for manifolds with iterated conical singularities

    math.DG 2025-06 conditional novelty 7.0 of 10

    For spin manifolds with iterated conical singularities, scalar-mean curvature comparison forces equality and rigidity, and nonnegative scalar curvature implies nonnegative ADM mass.

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