On the nonuniqueness of surfaces with constant mean curvature spanning a given contour

DOI10.1007/BF00280429zbMath0678.49036MaRDI QIDQ1124106

Klaus Steffen

Publication date: 1986

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

Dirichlet problemisoperimetric inequalityPlateau problemRellich's conjecture

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10)

Related Items (20)

Obituary: Stefan Hildebrandt (1936--2015) ⋮ Remarks on the boundary curve of a constant mean curvature topological disc ⋮ A compactness theorem for weak solutions of higher-dimensional \(H\)-systems ⋮ Multiple surfaces of non-constant mean curvature ⋮ Large solutions for biharmonic maps in four dimensions ⋮ The existence of surfaces of constant mean curvature with free boundaries ⋮ MULTIPLE SOLUTIONS FOR THE DIRICHLET PROBLEM FOR H-SYSTEMS WITH SMALL H ⋮ The blow up analysis of solutions of the elliptic sinh-Gordon equation ⋮ EMBEDDED DISC-TYPE SURFACES WITH LARGE CONSTANT MEAN CURVATURE AND FREE BOUNDARIES ⋮ Multiple solutions ofH-systems and Rellich's conjecture ⋮ Area minimizing hypersurfaces with prescribed volume and boundary ⋮ Bubbles with prescribed mean curvature: the variational approach ⋮ The Dirichlet problem for \(H\)-systems with small boundary data: blowup phenomena and nonexistence results ⋮ The Dirichlet problem for the equation of prescribed mean curvature ⋮ Blow-up analysis for the prescribed mean curvature equation on \(\mathbb R^2\) ⋮ Construction of nodal bubbling solutions for the weighted sinh-Poisson equation ⋮ Boundary regularity for area minimizing currents with prescribed volume ⋮ Large H-surfaces via the mountain-pass-lemma ⋮ Convergence of solutions of H-systems or how to blow bubbles ⋮ Multiple solutions to the Plateau problem for nonconstant mean curvature

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