Some characterization, uniqueness and existence results for Euclidean graphs of constant mean curvature with planar boundary

Authors
Citation
J. Ripoll, Some characterization, uniqueness and existence results for Euclidean graphs of constant mean curvature with planar boundary, PAC J MATH, 198(1), 2001, pp. 175-196
Citations number
17
Categorie Soggetti
Mathematics
Journal title
PACIFIC JOURNAL OF MATHEMATICS
ISSN journal
00308730 → ACNP
Volume
198
Issue
1
Year of publication
2001
Pages
175 - 196
Database
ISI
SICI code
0030-8730(200103)198:1<175:SCUAER>2.0.ZU;2-T
Abstract
We establish the existence and uniqueness of solutions to the Dirichlet pro blem for the cmc surface equation, including the minimal one, for zero boun dary data, in certain domains of the plane. We obtain results that characte rize the sphere and cmc graphs among compact embedded cmc surfaces with pla nar boundary satisfying certain geometric conditions. We also find conditio ns that imply that a compact embedded cmc surface which is a graph near the boundary is indeed a global graph.