The convexity and the Gaussian curvature estimates for the level sets of harmonic functions on convex rings in space forms
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Publication:472006
DOI10.1007/s12220-012-9339-8zbMath1327.35078OpenAlexW2092060982MaRDI QIDQ472006
Publication date: 18 November 2014
Published in: The Journal of Geometric Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s12220-012-9339-8
Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)
Related Items (12)
Serrin-Type Overdetermined Problem in $\mathbb H^n$ ⋮ The convexity of the level sets of maximal strictly space-like hypersurfaces defined on 2-dimensional space forms ⋮ Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces ⋮ Gaussian curvature estimates for the convex level sets of minimal graphs revisited ⋮ 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 ⋮ Serrin-type overdetermined problems for Hessian quotient equations and Hessian quotient curvature equations ⋮ 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 ⋮ Gauss curvature estimates for the convex level sets of a minimal surface immersed in \(\mathbb R^{n+1}\) ⋮ Superharmonicity of curvature function for the convex level sets of harmonic functions
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