Gaussian Curvature Estimates for the Convex Level Sets of Solutions for Some Nonlinear Elliptic Partial Differential Equations

DOI10.4208/jpde.v25.n3.4zbMath1274.35153arXiv1003.2057OpenAlexW3146389181WikidataQ128311570 ScholiaQ128311570MaRDI QIDQ4928010

Peihe Wang, Wei Zhang

Publication date: 20 June 2013

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

Full work available at URL: https://arxiv.org/abs/1003.2057

zbMATH Keywords

maximum principle minimal surface semilinear elliptic equation convex level sets Gaussian curvature estimates

Mathematics Subject Classification ID

Maximum principles in context of PDEs (35B50) A priori estimates in context of PDEs (35B45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Semilinear elliptic equations (35J61) Quasilinear elliptic equations with mean curvature operator (35J93)

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Curvature estimates for the level sets of solutions to a class of Monge-Ampère equations ⋮ Convexity of level lines of maximal space-like hypersurfaces in Minkowski space ⋮ Gaussian curvature estimates for the convex level sets of minimal graphs revisited ⋮ Some geometrical properties of convex level sets of minimal graph on 2-dimensional Riemannian manifolds ⋮ On convexity of level sets of \(p\)-harmonic functions ⋮ The geometric properties of harmonic function on 2-dimensional Riemannian manifolds ⋮ Convexity of level sets of minimal graph on space form with nonnegative curvature ⋮ Geometric properties of level curves of harmonic functions and minimal graphs in 2-dimensional space forms ⋮ The concavity of the Gaussian curvature of the convex level sets of \(p\)-harmonic functions with respect to the height ⋮ Superharmonicity of curvature function for the convex level sets of harmonic functions

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