Mohammad N. Ivaki

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20242026

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math.DG2026

On the conjectured capillary Blaschke-SantalÃ³ inequality

Carlos Cabezas-Moreno, Yingxiang Hu, Mohammad N. Ivaki

We prove that the conjectured capillary Blaschke--SantalÃ³ inequality holds for any unconditional, strictly convex capillary hypersurface when $I^¸ \in (0, \frac{I ¨}{} 2)$ .…

math.DG2025

Capillary curvature images

Yingxiang Hu, Mohammad N. Ivaki

In this paper, we solve the even capillary $L_{p}$ -Minkowski problem for the range $- n < p < 1$ and $I^¸ \in (0, \frac{I ¨}{} 2)$ . Our approach is based on an iterative scheme that builds o…

math.DG2025

Capillary Christoffel-Minkowski problem

Yingxiang Hu, Mohammad N. Ivaki, Julian Scheuer

The result of Guan and Ma (Invent. Math. 151 (2003)) states that if $I ¨ ^{- 1/ k} : S^{n} \to (0, \infty)$ is spherically convex, then $I ¨ $ arises as the $I ¨ _{k}$ curvature (the $…

math.DG2025

Stability of the cone-volume measure with near constant density

Yingxiang Hu, Mohammad N. Ivaki

We prove that if the density of the cone-volume measure of a smooth, strictly convex body with respect to the spherical Lebesgue measure is nearly constant, then a homothetic copy…

math.DG2024

Yingxiang Hu, Mohammad N. Ivaki

In the first part of this paper, we study the following non-homogeneous, locally constrained inverse curvature flow in Euclidean space $R^{n + 1}$ , \begin{align*} \dot{x}=\l…

On the conjectured capillary Blaschke-SantalÃ³ inequality

Capillary curvature images

Capillary Christoffel-Minkowski problem

Stability of the cone-volume measure with near constant density

New quermassintegral and PoincarÃ© type inequalities for non-convex domains