Minkowski Valuations and Generalized Valuations

2015/07/20 by Schuster, Franz E., Wannerer, Thomas · 2 citations
#43A90 #52A22 #52B45 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1507.05412

Abstract

A convolution representation of continuous translation invariant and SO(n) equivariant Minkowski valuations is established. This is based on a new classification of translation invariant generalized spherical valuations. As applications, Crofton and kinematic formulas for Minkowski valuations are obtained.

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• Ball-convex bodies and L_p relative surface areas
• Mixed Christoffel-Minkowski problems for bodies of revolution

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