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On Gromov's dihedral extremality and rigidity conjectures

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arxiv 2112.01510 v6 pith:IVVFCBAQ submitted 2021-12-02 math.DG math.KT

Jinmin Wang , Zhizhang Xie , Guoliang Yu This is my paper · ORCID
classification math.DGmath.KT
keywords dihedralboundarygromovmanifoldspolyhedralconjecturecurvaturesdimensions
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In this paper, we develop a new index theory for manifolds with polyhedral boundary. As an application, we prove Gromov's dihedral extremality conjecture regarding comparisons of scalar curvatures, mean curvatures and dihedral angles between two compact manifolds with polyhedral boundary in all dimensions. We also prove Gromov's dihedral rigidity conjecture for a class of positively curved manifolds with polyhedral boundary in all dimensions.

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Cited by 3 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.

  3. Gap phenomenon for scalar curvature

    math.DG 2025-01 conditional novelty 6.0 of 10

    Scalar curvature on any closed even-dimensional manifold with nonzero Euler characteristic can be increased by at most an explicit constant, the gap, which is a function of the minimal eigenvalue of the curvature oper...

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