Some geometrical properties of convex level sets of minimal graph on 2-dimensional Riemannian manifolds

DOI10.1016/j.na.2015.09.021zbMath1329.53088OpenAlexW2170133612WikidataQ115342922 ScholiaQ115342922MaRDI QIDQ898351

Peihe Wang, Ling-Ling Zhao

Publication date: 8 December 2015

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2015.09.021

zbMATH Keywords

curvature estimatelevel setsminimal graph

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 (11)

Decay rate and energy gap for the singularity solution of the inhomogeneous Landau-Lifshitz equation on \(\mathbb{S}^2\) ⋮ The convexity of the level sets of maximal strictly space-like hypersurfaces defined on 2-dimensional space forms ⋮ Uniqueness of conservative solutions to the generalized Camassa-Holm equation via characteristics ⋮ Convexity of level lines of maximal space-like hypersurfaces in Minkowski space ⋮ Unnamed Item ⋮ Curvature estimate of steepest descents of 2-dimensional maximal space-like hypersurfaces on space forms ⋮ Energy decay rate of multidimensional inhomogeneous Landau-Lifshitz-Gilbert equation and Schrödinger map equation on the sphere ⋮ HIGH-ORDER COPOSITIVE TENSORS AND ITS APPLICATIONS ⋮ ESTIMATE FOR EVOLUTIONARY SURFACES OF PRESCRIBED MEAN CURVATURE AND THE CONVERGENCE ⋮ Convexity of level sets of minimal graph on space form with nonnegative curvature ⋮ A new generalised two-component Camassa-Holm type system with waltzing peakons and wave breaking

Cites Work

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• The convexity and the Gaussian curvature estimates for the level sets of harmonic functions on convex rings in space forms
• A microscopic convexity theorem of level sets for solutions to elliptic equations
• The concavity of the Gaussian curvature of the convex level sets of \(p\)-harmonic functions with respect to the height
• The concavity of the Gaussian curvature of the convex level sets of minimal surfaces with respect to the height
• Convexity estimates for level sets of quasiconcave solutions to fully nonlinear elliptic equations
• A constant rank theorem for quasiconcave solutions of fully nonlinear partial differential equations
• Gaussian curvature estimates for the convex level sets of p-harmonic functions
• Curvature of Level Curves of Harmonic Functions
• Convexity properties of solutions to some classical variational problems
• Gaussian Curvature Estimates for the Convex Level Sets of Solutions for Some Nonlinear Elliptic Partial Differential Equations
• Conexity Of Level Sets For Solutions To elliptic Ring Problems
• On minimal surfaces bounded by two convex curves in parallel planes

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