Polyhedral Gauss-Bonnet theorems and valuations

DOI10.1007/s13366-017-0364-4zbMath1395.52016arXiv1708.05213OpenAlexW2963237982MaRDI QIDQ1646647

Rolf Schneider

Publication date: 25 June 2018

Published in: Beiträge zur Algebra und Geometrie (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.05213

zbMATH Keywords

polyhedronGauss-Bonnet theoremvaluationcritical point theorempolyhedral curvature

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Dissections and valuations (Hilbert's third problem, etc.) (52B45) Polyhedral manifolds (52B70)

Cites Work

• On combinatorial Gauss-Bonnet theorem for general Euclidean simplicial complexes
• Algebraic vertices of non-convex polyhedra
• Lipschitz-Killing curvatures of angular partially ordered sets
• Smooth approximation of polyhedral surfaces regarding curvatures
• Descartes' theorem in \(n\) dimensions
• The Gram-Sommerville and Gauss-Bonnet theorems and combinatorial geometric measures for noncompact polyhedra
• Kritische Punkte und Krümmung für die Mengen des Konvexringes
• Ein kombinatorisches Anologon zum Satz von Gauss-Bonnet
• The angle defect for arbitrary polyhedra
• The incidence algebra of polyhedra over the Minkowski algebra
• On the curvature of piecewise flat spaces
• Intrinsic volumes of polyhedral cones: a combinatorial perspective
• Generalized curvatures
• Critical points and curvature for embedded polyhedra
• Eckenkrümmung beliebiger kompakter euklidischer Polyeder und Charakteristik von Euler-Poincaré
• Curvature Measures
• Non-linear angle-sum relations for polyhedral cones and polytopes
• Convex Bodies The Brunn-MinkowskiTheory

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