The Hadwiger theorem on convex functions. IV: The Klain approach

DOI10.1016/j.aim.2022.108832OpenAlexW4312220946WikidataQ123264282 ScholiaQ123264282MaRDI QIDQ2679888

Monika Ludwig, Andrea Colesanti, Fabian Mussnig

Publication date: 26 January 2023

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.11565

zbMATH Keywords

convex functionvaluationHadwiger's theoremKlain-Schneider theorem

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Convex functions and convex programs in convex geometry (52A41) Mixed volumes and related topics in convex geometry (52A39) Convexity of real functions of several variables, generalizations (26B25) Dissections and valuations (Hilbert's third problem, etc.) (52B45)

Related Items (2)

Monge-Ampère operators and valuations ⋮ Equivariant endomorphisms of convex functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Laplace transforms and valuations
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• Minkowski areas and valuations
• Fisher information and matrix-valued valuations
• Hermitian integral geometry
• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• Integral and current representation of Federer's curvature measures
• Hessian measures. I
• On surface area measures of convex bodies
• Continuous rotation invariant valuations on convex sets
• Ellipsoids and matrix-valued valuations
• Minkowski valuations on convex functions
• Volume, polar volume and Euler characteristic for convex functions
• Hessian measures. II
• The support of dually epi-translation invariant valuations on convex functions
• The Hadwiger theorem on convex functions. III: Steiner formulas and mixed Monge-Ampère measures
• A homogeneous decomposition theorem for valuations on convex functions
• Continuous valuations on the space of Lipschitz functions on the sphere
• A class of invariant valuations on \(\operatorname{Lip}(S^{n -1})\)
• Valuations on convex functions and convex sets and Monge-Ampère operators
• Theory of valuations on manifolds. I: Linear spaces
• Convex valuations invariant under the Lorentz group
• Radial continuous rotation invariant valuations on star bodies
• Valuations on Sobolev spaces
• Valuations on Lp-Spaces
• The Centro-Affine Hadwiger Theorem
• The Gauss Image Problem
• Hessian valuations
• Variational Analysis
• A short proof of Hadwiger's characterization theorem
• Simple valuations on convex bodies
• Steiner type formulae and weighted measures of singularities for semi-convex functions
• Invariant Valuations on Super-Coercive Convex Functions
• Valuations on Convex Functions
• Convex Bodies The Brunn-MinkowskiTheory
• Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture

This page was built for publication: The Hadwiger theorem on convex functions. IV: The Klain approach