Valuations on Convex Functions

Abstract

All continuous, SL$(n)$ and translation invariant valuations on the space of convex functions on ${\mathbb{R}}^n$ are completely classified.

References in corpus (2)

• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• Laplace transforms and valuations

Cited by in corpus (23)

• Minkowski valuations on convex functions
• A homogeneous decomposition theorem for valuations on convex functions
• The support of dually epi-translation invariant valuations on convex functions
• Volume, Polar Volume and Euler Characteristic for Convex Functions
• Hessian valuations
• The Hadwiger theorem on convex functions, IV: The Klain approach
• The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge-Ampère measures
• The Hadwiger theorem on convex functions, I
• $\mathrm{SL}(n)$ invariant valuations on super-coercive convex functions
• Valuations on Log-Concave Functions
• Equivariant Endomorphisms of Convex Functions
• Valuations on Convex Bodies and Functions
• Additive kinematic formulas for convex functions
• Metrics and Isometries for Convex Functions
• Geometric valuation theory
• The Loewner function of a log-concave function
• Inequalities and counterexamples for functional intrinsic volumes and beyond
• A Riesz representation theorem for log-concave functions
• A Klain-Schneider Theorem for Vector-Valued Valuations on Convex Functions
• Dual curvature measures on convex functions and associated Minkowski problems
• The Legendre transform, the Laplace transform and valuations
• Notes on the functional LYZ ellipsoid
• Affine invariant maps for log-concave functions