Convex Polytopes, Dihedral Angles, Mean Curvature and Scalar Curvature

Misha Gromov

doi:10.1007/s00454-024-00657-7

Convex Polytopes, Dihedral Angles, Mean Curvature and Scalar Curvature

Misha Gromov

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We approximate boundaries of convex polytopes X⊂Rⁿ by smooth hypersurfaces Y=Y_ε with positive mean curvatures and, by using basic geometric relations between the scalar curvatures of Riemannian manifolds and the mean curvatures of their boundaries, establish lower bound on the dihedral angles of X.

Original language	English (US)
Pages (from-to)	849-875
Number of pages	27
Journal	Discrete and Computational Geometry
Volume	72
Issue number	2
DOIs	https://doi.org/10.1007/s00454-024-00657-7
State	Published - Sep 2024

Keywords

52A20
52B70
53C20
53C23
Approximation theorems
Geometric measure theory
Polytopes
Riemannian manifolds

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-024-00657-7

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abstract = "We approximate boundaries of convex polytopes X⊂Rn by smooth hypersurfaces Y=Yε with positive mean curvatures and, by using basic geometric relations between the scalar curvatures of Riemannian manifolds and the mean curvatures of their boundaries, establish lower bound on the dihedral angles of X.",

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author = "Misha Gromov",

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AB - We approximate boundaries of convex polytopes X⊂Rn by smooth hypersurfaces Y=Yε with positive mean curvatures and, by using basic geometric relations between the scalar curvatures of Riemannian manifolds and the mean curvatures of their boundaries, establish lower bound on the dihedral angles of X.

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KW - 53C23

KW - Approximation theorems

KW - Geometric measure theory

KW - Polytopes

KW - Riemannian manifolds

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Convex Polytopes, Dihedral Angles, Mean Curvature and Scalar Curvature

Abstract

Keywords

ASJC Scopus subject areas

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