Convex polytopes, dihedral angles, mean curvature and scalar curvature
type: Item
instance of: scholarly article
title: Convex polytopes, dihedral angles, mean curvature and scalar curvature
author: Misha Gromov
published in: Discrete \& Computational Geometry
publication date: 2024-10-25T00:00:00Z
review text: This deep and interesting paper derives lower bounds on the dihedral angles of polytopes in \(\mathbb{R}^d\) by applying techniques from differential geometry to smooth approximating bodies, and constructs some interesting examples of polytopes with nontrivial upper bounds on their dihedral angles.\N\NThe reader is warned that the notation is sometimes nonconventional (\textit{e.g.}, bullet points with subscripts) and challenging to follow (both the regular hexagon and the regular octagon appear as symbols, at a point size that makes them hard to distinguish.) The word ``complement[ary]'' is used where ``supplement[ary]'' would be customary.
reviewed by: Robert Dawson
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52B70
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C23
zbMATH DE Number: 7931803
zbMATH Keywords: geometric measure theory
zbMATH Keywords: approximation theorems
zbMATH Keywords: polytopes
zbMATH Keywords: Riemannian manifolds
MaRDI profile type: Publication
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DOI: 10.1007/S00454-024-00657-7
description: scientific article; zbMATH DE number 7931803