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The Dirichlet Problem for constant mean curvature graphs in M×R

Abigail Folha and Harold Rosenberg

Geometry & Topology 16 (2012) 1171–1203

DOI: 10.2140/gt.2012.16.1171
Abstract

We study graphs of constant mean curvature H > 0 in M × R for M a Hadamard surface, ie a complete simply connected surface with curvature bounded above by a negative constant −a. We find necessary and sufficient conditions for the existence of these graphs over bounded domains in M, having prescribed boundary data, possibly infinite.

Keywords

Hadamard surface, constant mean curvature, Dirichlet problem
Mathematical Subject Classification

Primary: 53A10

Secondary: 53C42
References
Publication

Received: 21 February 2011
Revised: 5 March 2012
Accepted: 10 April 2012
Published: 23 June 2012
Proposed: Tobias H Colding
Seconded: John Lott, Yasha Eliashberg
Authors
Abigail Folha
Instituto de Matemática – Departamento de Geometria
Universidade Federal Fluminense
R Mário Santos Braga, s/n
Campus do Valonguinho
CEP 24020-140 Niterói, RJ
Brazil
Harold Rosenberg
Instituto de Matemática Pura e Aplicada
Estrada Dona Castorina 110
CEP 22460-320 Rio de Janeiro, RJ
Brazil
http://www.math.jussieu.fr/~rosen/