The Hadwiger theorem on convex functions, I

Abstract

A complete classification of all continuous, epi-translation and rotation invariant valuations on the space of super-coercive convex functions on ${\mathbb{R}}^n$ is established. The valuations obtained are functional versions of the classical intrinsic volumes. For their definition, singular Hessian valuations are introduced.

References in corpus (5)

• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• The Hadwiger theorem on convex functions, IV: The Klain approach
• The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge-Ampère measures
• Functional inequalities derived from the Brunn-Minkowski inequalities for quermassintegrals
• A Riesz representation theorem for log-concave functions

Cited by in corpus (6)

• Additive kinematic formulas for convex functions
• Metrics and Isometries for Convex Functions
• A Riesz representation theorem for log-concave functions
• A Klain-Schneider Theorem for Vector-Valued Valuations on Convex Functions
• Inequalities and counterexamples for functional intrinsic volumes and beyond
• The Legendre transform, the Laplace transform and valuations