Crofton measures and Minkowski valuations

Abstract

A description of continuous rigid motion compatible Minkowski valuations is established. As an application, we present a Brunn-Minkowski type inequality for intrinsic volumes of these valuations.

Cited by in corpus (30)

• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• The dual Minkowski problem for negative indices
• On the inverse Klain map
• Kinematic formulas for tensor valuations
• $L_p$ Minkowski Valuations on polytopes
• Classification of invariant valuations on the quaternionic plane
• The dual Minkowski problem for symmetric convex bodies
• $L_p$-Blaschke Valuations
• Minkowski valuations in a 2-dimensional complex vector space
• Rényi Divergence and $L_p$-affine surface area for convex bodies
• $\mathrm{SL}(\mathrm{n})$ covariant function-valued valuations
• Uniqueness of curvature measures in pseudo-Riemannian geometry
• The Lp Minkowski problem for polytopes for negative p
• Kinematic formulae for tensorial curvature measures
• The Loewner function of a log-concave function
• SL(n)-Covariant $L_p$-Minkowski Valuations
• SL($n$) contravariant vector valuations
• Minkowski additive operators under volume constraints
• Contact measures in isotropic spaces
• Affine function valued valuations
• The Centro-Affine Hadwiger Theorem
• Integral geometry of exceptional spheres
• The Minkowski problem in the Gaussian probability space
• Affine invariant maps for log-concave functions
• Relative entropies for convex bodies
• The Legendre transform, the Laplace transform and valuations
• Orlicz hormonic Blaschke addition
• $L_p$-Steiner quermassintegrals
• The dual Orlicz-Aleksandrov-Fenchel inequality
• Grassmann measures of convex bodies