Uniqueness for certain surfaces of prescribed mean curvature
type: Item
instance of: scholarly article
title: Uniqueness for certain surfaces of prescribed mean curvature
zbMATH Open document ID: 0621.58008
author: Thomas I. Vogel
published in: Pacific Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: This paper deals with a problem which arises naturally from the classical problem of the shape of the free surface of a liquid in a capillary tube. The usual approach has been to consider absolute minima of the relevant energy functional, to show that an absolute minimum has a free surface which is the graph of a function satisfying a nonlinear partial differential equation, and to then apply uniqueness theorems for such functions. The present paper weakens these hypotheses by considering relative minima (in the setting of BV theory) and stationary points (in a classical differential geometry setting). In both cases the surface has prescribed mean curvature which is nondecreasing with height, and satisfies a contact angle condition. Under these weakened hypotheses, uniqueness still holds, so that no new surfaces are found.
Mathematics Subject Classification ID: 58E15
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 49Q05
zbMATH DE Number: 4007279
zbMATH Keywords: energy functional
zbMATH Keywords: prescribed mean curvature
MaRDI profile type: Publication
full work available at URL: pjm.1988.134.197
OpenAlex ID: W2022569093
DOI: 10.2140/PJM.1988.134.197
description: scientific article; zbMATH DE number 4007279