Cabezas Moreno, C., Hu, Y., & Ivaki, M. N. (2025). On the conjectured capillary Blaschke-Santaló inequality. arXiv. https://doi.org/10.48550/arXiv.2509.20257
E104-06 - Forschungsbereich Konvexe und Diskrete Geometrie
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ArXiv ID:
2509.20257
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Date (published):
24-Sep-2025
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Number of Pages:
14
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Preprint Server:
arXiv
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Keywords:
Capillary Geometry, Blaschke-Santaló inequality
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Abstract:
We prove that the conjectured capillary Blaschke--Santal\'{o} inequality holds for any unconditional, strictly convex capillary hypersurface when $\theta \in \left(0, \tfrac{\pi}{2}\right)$. Moreover, for $\theta \in \left(\tfrac{\pi}{2}, \pi\right)$, we show that the capillary volume product has no finite upper bound.
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Project title:
Existenz und Eindeutigkeit von Lösungen für Krümmungsprobleme: P 36545-N (FWF - Österr. Wissenschaftsfonds)
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Project (external):
National Key Re- search and Development Program of China
