On the conjectured capillary Blaschke-Santaló inequality

2025/09/24 by Cabezas-Moreno, Carlos, Hu, Yingxiang, Ivaki, Mohammad N.
#Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2509.20257

Abstract

We prove that the conjectured capillary Blaschke-Santaló inequality holds for any unconditional, strictly convex capillary hypersurface when θ∈ (0, \tfracπ2). Moreover, for θ∈ (\tfracπ2, π), we show that the capillary volume product has no finite upper bound.

Citations

• The capillary Gauss curvature flow
• On weighted Blaschke--Santalo and strong Brascamp--Lieb inequalities
• Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary II
• A quantitative stability result for the Prékopa-Leindler inequality for arbitrary measurable functions
• Centro-Affine Differential Geometry and the Log-Minkowski Problem
• Stability of the Prekopa-Leindler inequality for log-concave functions
• Some functional forms of Blaschke-Santaló inequality

Related

• Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundary II
• Alexandrov-Fenchel inequalities for capillary hypersurfaces in hyperbolic space
• Some functional forms of Blaschke-Santaló inequality
• Hypercontractivity beyond Nelson's time and its applications to Blaschke--Santaló inequality and inverse Santaló inequality
• A Blaschke-Santaló inequality for unconditional log-concave measures