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

Abstract

New proofs of the Hadwiger theorem for smooth and for continuous valuations on convex functions are obtained, and the Klain-Schneider theorem on convex functions is established. In addition, an extension theorem for valuations defined on functions with lower dimensional domains is proved, and its connection to the Abel transform is explained.

References in corpus (2)

• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge-Ampère measures

Cited by in corpus (6)

• Equivariant Endomorphisms of Convex Functions
• Additive kinematic formulas for convex functions
• Valuations on Convex Bodies and 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