Brauner, L., Hofstätter, G. C., & Ortega Moreno, O. A. (2025). The Christoffel problem for the disk area measure. arXiv. https://doi.org/10.48550/ARXIV.2508.09800
Christoffel problem; mixed area measures; Kubota formulas
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Abstract:
The mixed Christoffel problem asks for necessary and sufficient conditions for a Borel measure on the Euclidean unit sphere to be the mixed area measure of some convex bodies, all but one of them are fixed. We provide a solution in the case where the fixed reference bodies are (n-1)-dimensional disks with parallel axes and the measure has no mass at the poles of the sphere determined by this axis.
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Project title:
Bewertungen auf konvexen Funktionen: P 34446-N (FWF - Österr. Wissenschaftsfonds) Fixpunkt Probleme und isoperimetrische Ungleichungen: ESP 236-N (FWF - Österr. Wissenschaftsfonds)
