Minkowski valuations on convex functions

Abstract

A classification of SL$(n)$ contravariant Minkowski valuations on convex functions and a characterization of the projection body operator are established. The associated LYZ measure is characterized. In addition, a new SL$(n)$ covariant Minkowski valuation on convex functions is defined and characterized.

References in corpus (7)

• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• Valuations on Convex Functions
• Minkowski valuations on convex functions
• Laplace transforms and valuations
• $L_p$ Minkowski Valuations on polytopes
• GL(n) contravariant Minkowski valuations
• Translation invariant valuations on quasi-concave functions

Cited by in corpus (24)

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• 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
• $\mathrm{SL}(\mathrm{n})$ covariant function-valued valuations
• Valuations on Log-Concave Functions
• Equivariant Endomorphisms of Convex Functions
• Valuations on Convex Bodies and Functions
• Metrics and Isometries for Convex Functions
• Geometric valuation theory
• The Loewner function of a log-concave function
• A Riesz representation theorem for log-concave functions
• A Klain-Schneider Theorem for Vector-Valued Valuations on Convex Functions
• Dot product invariant valuations on Lip$(S^{n-1})$
• Affine function valued valuations
• $\mathrm{SL}(n)$ contravariant function-valued valuations on polytopes
• Dual curvature measures on convex functions and associated Minkowski problems
• The Legendre transform, the Laplace transform and valuations
• Affine invariant maps for log-concave functions