On minimal surfaces bounded by two convex curves in parallel planes

DOI10.1016/0022-0396(87)90131-8zbMath0626.53002OpenAlexW1981179572MaRDI QIDQ5893773

Marco Longinetti

Publication date: 1987

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(87)90131-8

zbMATH Keywords

maximum principleminimal surfacecathenoid type problemsestimate for the curvature

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Maximum principles in context of PDEs (35B50)

Related Items (22)

Curvature estimates for the level sets of solutions to a class of Monge-Ampère equations ⋮ The convexity of the level sets of maximal strictly space-like hypersurfaces defined on 2-dimensional space forms ⋮ On the microscopic spacetime convexity principle for fully nonlinear parabolic equations II: Spacetime quasiconcave solutions ⋮ On the Hessian matrix and Minkowski addition of quasiconvex functions ⋮ Convexity of level lines of maximal space-like hypersurfaces in Minkowski space ⋮ Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces ⋮ Curvature estimate of steepest descents of 2-dimensional maximal space-like hypersurfaces on space forms ⋮ Some geometrical properties of convex level sets of minimal graph on 2-dimensional Riemannian manifolds ⋮ Topological bounds for Fourier coefficients and applications to torsion ⋮ Isoperimetric inequalities and regularity of \(a\)-harmonic functions on surfaces ⋮ On convexity of level sets of \(p\)-harmonic functions ⋮ The geometric properties of harmonic function on 2-dimensional Riemannian manifolds ⋮ Isoperimetric inequalities for the length of level lines of solutions of quasilinear capacity problems in the plane ⋮ The convexity and the Gaussian curvature estimates for the level sets of harmonic functions on convex rings in space forms ⋮ Curvature estimates for the level sets of spatial quasiconcave solutions to a class of parabolic equations ⋮ Gaussian curvature estimates for the convex level sets of p-harmonic functions ⋮ Convexity of level sets of minimal graph on space form with nonnegative curvature ⋮ The concavity of the Gaussian curvature of the convex level sets of \(p\)-harmonic functions with respect to the height ⋮ Gauss curvature estimates for the convex level sets of a minimal surface immersed in \(\mathbb R^{n+1}\) ⋮ Counterexample to the convexity of level sets of solutions to the mean curvature equation ⋮ On the convexity of geometric functionals of level for solutions of certain elliptic partial differential equations ⋮ Curvature estimates in dimensions 2 and 3 for the level sets of $p$-harmonic functions in convex rings

Cites Work

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• On surfaces of stationary area bounded by two circles, or convex curves, in parallel planes
• Ein Einschließungssatz für Minimalflächen
• Subfunction and second-order ordinary differential inequalities
• Maximum principles for minimal surfaces and for surfaces of continuous mean curvature
• Note on the Nonexistence of Minimal Surfaces
• The Calculus of Variations for Multiple Integrals

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