E104-06 - Forschungsbereich Konvexe und Diskrete Geometrie
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ArXiv ID:
2403.06697
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Date (published):
11-Mar-2024
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Number of Pages:
23
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Preprint Server:
arXiv
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Keywords:
integral geometry; additive kinematic formula; convex function; valuation; mixed Monge-Ampère measure; mixed area measure
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Abstract:
We prove a functional version of the additive kinematic formula as an application of the Hadwiger theorem on convex functions together with a Kubota-type formula for mixed Monge-Ampère measures. As an application, we give a new explanation for the equivalence of the representations of functional intrinsic volumes as singular Hessian valuations and as integrals with respect to mixed Monge-Ampère measures. In addition, we obtain a new integral geometric formula for mixed area measures of convex bodies, where integration on SO(n−1)×O(1) is considered.
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Project title:
Hessische Ungleichungen und Erweiterungen auf Sobolev-Räumen: J 4490 (FWF - Österr. Wissenschaftsfonds) Integralgeometrie auf konvexen Funktionen: P 36210 (FWF - Österr. Wissenschaftsfonds) Bewertungen auf konvexen Funktionen: P 34446-N (FWF - Österr. Wissenschaftsfonds)
