On Convexity of Level Curves of Harmonic Functions in the Hyperbolic Plane

DOI10.2307/2159391zbMath0746.31002OpenAlexW4237356637MaRDI QIDQ3987606

Michael Papadimitrakis

Publication date: 28 June 1992

Full work available at URL: https://doi.org/10.2307/2159391

zbMATH Keywords

convexityPoincaré metric

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Spherical and hyperbolic convexity (52A55) Convex sets in (2) dimensions (including convex curves) (52A10)

Related Items (6)

Length and area estimates for (hyperbolically) convex conformal mappings ⋮ Conformal mapping, convexity and total absolute curvature ⋮ The convexity of the level sets of maximal strictly space-like hypersurfaces defined on 2-dimensional space forms ⋮ Curvature estimate of steepest descents of 2-dimensional maximal space-like hypersurfaces on space forms ⋮ The convexity and the Gaussian curvature estimates for the level sets of harmonic functions on convex rings in space forms ⋮ Convexity of level sets of minimal graph on space form with nonnegative curvature

Cites Work

• Unnamed Item
• Convexity of solutions of semilinear elliptic equations
• Convex solutions of certain elliptic equations have constant rank Hessians
• A maximum principle for sums of subharmonic functions, and the convexity of level sets
• Capacitary functions in convex rings
• An Extended Principle of the Maximum for Harmonic Functions in 3-Dimensions
• A Result Concerning Convex Level Surfaces of 3-Dimensional Harmonic Functions
• Further Results Concerning the Level Surfaces of the Green's Function for a 3-Dimensional Convex Domain (I)
• Note on the Green Function of a Star-Shaped Three Dimensional Region
• Convexity properties of solutions to some classical variational problems

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