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

Folha, Abigail¹ ; Rosenberg, Harold²

¹ Instituto de Matemática – Departamento de Geometria, Universidade Federal Fluminense, R Mário Santos Braga, s/n, Campus do Valonguinho, CEP 24020-140 Niterói, RJ, Brazil
² Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, CEP 22460-320 Rio de Janeiro, RJ, Brazil

Geometry & topology, Tome 16 (2012) no. 2, pp. 1171-1203.

Résumé

We study graphs of constant mean curvature $H>0$ in $\mathbb{M}\times ℝ$ for $\mathbb{M}$ 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 $\mathbb{M}$, having prescribed boundary data, possibly infinite.

Détail

DOI : 10.2140/gt.2012.16.1171

Classification : 53A10, 53C42
Keywords: Hadamard surface, constant mean curvature, Dirichlet problem

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