Singular valuations and the Hadwiger theorem on convex functions

2022/09/12 by Jonas Knoerr, Knoerr, Jonas · 2 citations
Agricultural and Biological Sciences · Economics, Econometrics and Finance · Mathematics · #26B25 #52B45 #53C65 #African Botany and Ecology Studies #Economic theories and models #FOS: Mathematics #Mathematical Dynamics and Fractals #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2209.05158

openalex publication_date 2022/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a characterization of smooth, rotation and dually epi-translation invariant valuations and use this result to obtain a new proof of the Hadwiger theorem on convex functions. We also give a description of the construction of the functional intrinsic volumes using integration over the differential cycle and provide a new representation of these functionals as principal value integrals with respect to the Hessian measures.

Cited by

• Polynomial local functionals on convex functions
• Additive Kinematic Formulas for Functional Minkowski Vectors

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