The Hadwiger theorem on convex functions. III: Steiner formulas and mixed Monge-Ampère measures

DOI10.1007/s00526-022-02288-3OpenAlexW4285090751WikidataQ115236757 ScholiaQ115236757MaRDI QIDQ2159513

Fabian Mussnig, Andrea Colesanti, Monika Ludwig

Publication date: 1 August 2022

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.05648

zbMATH Keywords

convex functionvaluationMonge-Ampère measureSteiner formula

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 (3)

The Hadwiger theorem on convex functions. IV: The Klain approach ⋮ Monge-Ampère operators and valuations ⋮ Equivariant endomorphisms of convex functions

Cites Work

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• Laplace transforms and valuations
• The Monge-Ampère equation and its applications
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• Minkowski areas and valuations
• Fisher information and matrix-valued valuations
• Hermitian integral geometry
• Minkowski valuations intertwining the special linear group
• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• Mixed discriminants of positive semidefinite matrices
• Hessian measures. I
• Continuous rotation invariant valuations on convex sets
• Amoebas, Monge-Ampère measures, and triangulations of the Newton polytope
• Minkowski valuations on convex functions
• Volume, polar volume and Euler characteristic for convex functions
• Hessian measures. III
• Mixed integrals and related inequalities
• A characterization of affine surface area
• Hessian measures. II
• The support of dually epi-translation invariant valuations on convex functions
• 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
• Valuation theory of indefinite orthogonal groups
• Convex valuations invariant under the Lorentz group
• On the Hessian of a function and the curvature of its graph
• 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
• Equlibrium measure of a product subset of ℂⁿ
• 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
• The Monge-Ampère equation
• Description of translation invariant valuations on convex sets with solution of P. McMullen's conjecture

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