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arXiv · 2509.20257

On the conjectured capillary Blaschke-Santal\'o inequality

Carlos Cabezas-Moreno·Yingxiang Hu·Mohammad N. Ivaki
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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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Carlos Cabezas-Moreno, Yingxiang Hu, Mohammad N. Ivaki. 2025-09-24. On the conjectured capillary Blaschke-Santal\'o inequality. https://doi.org/10.1112/mtk.70109

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