The $L_p$ dual Minkowski problem for capillary hypersurfaces

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Gao, Ya
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866918285292863488
author Gao, Ya
author_facet Gao, Ya
contents In this paper, we consider the $L_p$ dual Minkowski problem for capillary hypersurfaces for $p>q$ and $q\leq 1$, which aims to find a capillary convex body with a prescribed capillary $(p,q)$-th dual curvature measure in the Euclidean half-space. We reduce it to a Monge-Ampère type equation with a Robin boundary condition on the unit spherical cap, we prove that there exists a unique smooth solution that solves this problem provided $θ\in (0,\fracπ{2})$.
format Preprint
id arxiv_https___arxiv_org_abs_2510_12804
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The $L_p$ dual Minkowski problem for capillary hypersurfaces
Gao, Ya
Differential Geometry
Analysis of PDEs
In this paper, we consider the $L_p$ dual Minkowski problem for capillary hypersurfaces for $p>q$ and $q\leq 1$, which aims to find a capillary convex body with a prescribed capillary $(p,q)$-th dual curvature measure in the Euclidean half-space. We reduce it to a Monge-Ampère type equation with a Robin boundary condition on the unit spherical cap, we prove that there exists a unique smooth solution that solves this problem provided $θ\in (0,\fracπ{2})$.
title The $L_p$ dual Minkowski problem for capillary hypersurfaces
topic Differential Geometry
Analysis of PDEs
url https://arxiv.org/abs/2510.12804