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<p>We give a classification 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, originally established by Colesanti, Ludwig and Mussnig. 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.</p>

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Singular Valuations and the Hadwiger Theorem on Convex Functions

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Jonas Knoerr

摘要

We give a classification 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, originally established by Colesanti, Ludwig and Mussnig. 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.