Valuations on Convex Bodies and Functions

Abstract

An introduction to geometric valuation theory is given. The focus is on classification results for $\mathrm{SL}(n)$ invariant and rigid motion invariant valuations on convex bodies and on convex functions.

References in corpus (14)

• 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
• Hessian valuations
• Affine invariant valuations on polytopes
• The Hadwiger theorem on convex functions, IV: The Klain approach
• Radial continuous rotation invariant valuations on star bodies
• Real-valued valuations on Sobolev spaces
• The Hadwiger theorem on convex functions, III: Steiner formulas and mixed Monge-Ampère measures
• $\mathrm{SL}(n)$ invariant valuations on super-coercive convex functions
• Valuations on Log-Concave Functions

Cited by in corpus (1)

• A Klain-Schneider Theorem for Vector-Valued Valuations on Convex Functions