Constant Mean Curvature Graphs on Unbounded Convex Domains
Author: López, R.
Source: Journal of Differential Equations, Volume 171, Number 1, March 2001 , pp. 54-62(9)
Publisher: Academic Press
Abstract:In this paper, we consider the Dirichlet problem for the constant mean curvature equation on an unbounded convex planar domain Ω. Let H>0. We prove that there exists a graph with constant mean curvature H and with boundary ∂Ω if and only if Ω is included in an infinite strip of width 1H. We also establish an existence result for convex bounded domains contained in a strip. Copyright 2001 Academic Press.
Document Type: Research Article
Affiliations: Departamento de Geometría y Topología, Universidad de Granada, Granada, 18071, Spain
Publication date: March 1, 2001