A polyhedron comparison theorem for 3-manifolds with positive scalar curvature

Research output: Contribution to journalArticle

Abstract

The study of comparison theorems in geometry has a rich history. In this paper, we establish a comparison theorem for polyhedra in 3-manifolds with nonnegative scalar curvature, answering affirmatively a dihedral rigidity conjecture by Gromov. For a large collections of polyhedra with interior non-negative scalar curvature and mean convex faces, we prove the dihedral angles along its edges cannot be everywhere less or equal than those of the corresponding Euclidean model, unless it is isometric to a flat polyhedron.

Original languageEnglish (US)
JournalInventiones Mathematicae
Volume219
Issue number1
DOIs
StatePublished - Jan 1 2020
Externally publishedYes

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Positive Scalar Curvature
Comparison Theorem
Polyhedron
Nonnegative Curvature
Scalar Curvature
Dihedral angle
Isometric
Rigidity
Euclidean
Interior
Face
Model

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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A polyhedron comparison theorem for 3-manifolds with positive scalar curvature. / Li, Chao.

In: Inventiones Mathematicae, Vol. 219, No. 1, 01.01.2020.

Research output: Contribution to journalArticle

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