Capillary surfaces of constant mean curvature in a right solid cylinder

TL;DR

This paper studies constant mean curvature surfaces within a right cylinder that meet the boundary at a fixed angle, revealing symmetry properties and conditions under which the surfaces are planar or catenoidal.

Contribution

It provides new symmetry results and characterizations of constant mean curvature surfaces in cylinders, including conditions for planar or catenoidal shapes.

Findings

Surfaces inside the cylinder exhibit symmetry via Alexandrov reflection.

Zero mean curvature surfaces are characterized as planes or catenoids under certain conditions.

The paper extends understanding of boundary behavior of constant mean curvature surfaces.

Abstract

In this paper we investigate constant mean curvature surfaces with nonempty boundary in Euclidean space that meet a right cylinder at a constant angle along the boundary. If the surface lies inside of the cylinder, we obtain some results of symmetry by using the Alexandrov reflection method. When the mean curvature is zero, we give sufficient conditions to obtain that the surface is part of a plane or a catenoid.