Some existence and nonexistence theorems for compact graphs of constant mean curvature with boundary in parallel planes.

DOI10.1007/BF02930757zbMath1041.53006OpenAlexW2052937418MaRDI QIDQ1608510

Jaime Bruck Ripoll, Nedir do Espírito-Santo

Publication date: 8 August 2002

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02930757

zbMATH Keywords

CMC graphcompact graphs

Mathematics Subject Classification ID

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

Related Items (5)

Compact minimal vertical graphs with non-connected boundary in \(\mathbb{H}^{n}\times\mathbb{R}\) ⋮ WETTING PHENOMENA AND CONSTANT MEAN CURVATURE SURFACES WITH BOUNDARY ⋮ Compact CMC graphs in \(M\times\mathbb{R}\) with boundary in two horizontal slices ⋮ Some existence results about radial graphs of constant mean curvature with boundary in parallel planes ⋮ A note on doubly connected surfaces of constant mean curvature with prescribed boundary

Cites Work

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• Maximum principles and nonexistence results for minimal submanifolds
• Constant mean curvature surfaces in a half-space of \(\mathbb{R}^ 3\) with boundary in the boundary of the half-space
• Curvature estimates and compactness theorems in 3-manifolds for surfaces that are stationary for parametric elliptic functionals
• Existence and nonexistence for the exterior Dirichlet problem for the minimal surface equation in the plane.
• Maximum principles for minimal surfaces in \(\mathbb{R}^ 3\) having noncompact boundary and a uniqueness theorem for the helicoid
• Some characterization, uniqueness and existence results for Euclidean graphs of constant mean curvature with planar boundary.

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