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

Abstract

A complete family of functional Steiner formulas is established. As applications, an explicit representation of functional intrinsic volumes using special mixed Monge-Ampère measures and a new version of the Hadwiger theorem on convex functions are obtained.

References in corpus (12)

• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• Valuations on Convex Functions
• Minkowski valuations on convex functions
• A homogeneous decomposition theorem for valuations on convex functions
• Laplace transforms and valuations
• The support of dually epi-translation invariant valuations on convex functions
• Volume, Polar Volume and Euler Characteristic for Convex Functions
• Valuation theory of indefinite orthogonal groups
• Hessian valuations
• The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge-Ampère measures
• Radial continuous rotation invariant valuations on star bodies
• $\mathrm{SL}(n)$ invariant valuations on super-coercive convex functions

Cited by in corpus (8)

• 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
• Equivariant Endomorphisms of Convex Functions
• Valuations on Convex Bodies and Functions
• Additive kinematic formulas for convex functions
• Inequalities and counterexamples for functional intrinsic volumes and beyond
• The Legendre transform, the Laplace transform and valuations