On the extendability by continuity of angular valuations on polytopes

DOI10.1016/j.jfa.2020.108665zbMath1452.52010arXiv1907.11606OpenAlexW3033595659MaRDI QIDQ2192341

Thomas Wannerer

Publication date: 17 August 2020

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.11606

zbMATH Keywords

polytopeconvex setvaluation

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Mixed volumes and related topics in convex geometry (52A39) Dissections and valuations (Hilbert's third problem, etc.) (52B45) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (2)

The zonoid algebra, generalized mixed volumes, and random determinants ⋮ From harmonic analysis of translation-invariant valuations to geometric inequalities for convex bodies

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the inverse Klain map
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• A Fourier-type transform on translation-invariant valuations on convex sets
• Weakly continuous valuations on convex polytopes
• Valuations on manifolds and integral geometry
• Hermitian integral geometry
• Kinematische Berührmaße für konvexe Körper
• On the extension of additive functionals on classes of convex sets
• Curvature measures of convex bodies
• Ellipsoids and matrix-valued valuations
• On P. McMullen's conjecture on translation invariant valuations
• Minkowski valuations and generalized valuations
• Hard Lefschetz theorem for valuations, complex integral geometry, and unitarily invariant valuations.
• The multiplicative structure on continuous polynomial valuations
• A characterization of affine surface area
• Local tensor valuations
• Valuation theory of indefinite orthogonal groups
• Crofton formulas and indefinite signature
• On extendability by continuity of valuations on convex polytopes
• Integral geometry of complex space forms
• Valuations and surface area measures
• Theory of valuations on manifolds. I: Linear spaces
• Theory of valuations on manifolds: A survey
• Convex valuations invariant under the Lorentz group
• Compact Lie Groups
• Intersection bodies and valuations
• Introduction to the Theory of Valuations
• Weighted floating bodies and polytopal approximation
• Even valuations on convex bodies
• EXTENSIONS OF TRANSLATION INVARIANT VALUATIONS ON POLYTOPES
• The Explicit Fourier Decomposition of L²SO(n)/SO(n - m))
• Algebraic Integral Geometry
• Rotation covariant local tensor valuations on convex bodies
• Convex Bodies The Brunn-MinkowskiTheory
• Theory of valuations on manifolds, III. Multiplicative structure in the general case
• Minkowski valuations
• Notions of convexity
• Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture

This page was built for publication: On the extendability by continuity of angular valuations on polytopes