Capillary Orlicz-Minkowski flow in the upper half-space

TL;DR

This paper investigates an anisotropic capillary Gauss curvature flow in the upper half-space, demonstrating its long-term behavior and convergence, leading to new existence results for the capillary Orlicz-Minkowski problem.

Contribution

It introduces a flow approach to solve the capillary Orlicz-Minkowski problem without requiring evenness, expanding the understanding of anisotropic curvature flows.

Findings

Flow converges to stationary solutions

Establishes existence of smooth solutions

Provides a new method for the Minkowski problem

Abstract

In this paper, we study the long-time existence and asymptotic behavior of an anisotropic capillary Gauss curvature flow. By studying this flow and proving its convergence to a stationary solution, we establish a new existence result for the capillary Orlicz-Minkowski problem without the evenness assumption, and provide a flow approach to the existence of smooth solutions.