The Dirichlet problem for constant mean curvature surfaces in Heisenberg space

DOI10.1007/s00526-007-0101-1zbMath1210.53010arXivmath/0612712OpenAlexW3099242264MaRDI QIDQ2385154

Marcos Dajczer, Luis J. Alías, Harold Rosenberg

Publication date: 11 October 2007

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612712

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Nonlinear elliptic equations (35J60) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (8)

Spacelike graphs of prescribed mean curvature in the steady state space ⋮ On the geometry of the Heisenberg group with a balanced metric ⋮ Extensions of the duality between minimal surfaces and maximal surfaces ⋮ Killing graphs with prescribed mean curvature ⋮ Minimal graphs in \(\mathrm{Nil}_3:\) existence and non-existence results ⋮ Fatou's theorem and minimal graphs ⋮ Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space ⋮ Killing graphs with prescribed mean curvature and Riemannian submersions

Cites Work

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• A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
• Isometric immersions into 3-dimensional homogeneous manifolds
• Minimal surfaces in \(M^2\times \mathbb{R}\)
• Invariant surfaces of the Heisenberg groups
• Elliptic partial differential equations of second order
• Constant mean curvature surfaces in homogeneously regular 3-manifolds
• Nonlinear second-order elliptic equations V. The dirichlet problem for weingarten hypersurfaces
• The problem of dirichlet for quasilinear elliptic differential equations with many independent variables

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