Existence and non-existence of minimal graphic and p-harmonic functions
| Autor: | Jean-Baptiste Casteras, Esko Heinonen, Ilkka Holopainen |
|---|---|
| Přispěvatelé: | Department of Mathematics and Statistics, Geometric Analysis and Partial Differential Equations, Département de mathématiques Université Libre de Bruxelles, Université libre de Bruxelles (ULB), Méthodes quantitatives pour les modèles aléatoires de la physique (MEPHYSTO-POST), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Department of Mathematics and Statistics [Helsinki], Falculty of Science [Helsinki], University of Helsinki-University of Helsinki, Helsingin yliopisto = Helsingfors universitet = University of Helsinki-Helsingin yliopisto = Helsingfors universitet = University of Helsinki, Casteras, Jean-Baptiste |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics General Mathematics 01 natural sciences 010104 statistics & probability THEOREMS GREENS-FUNCTIONS FOS: Mathematics 111 Mathematics Hadamard manifold Sectional curvature 0101 mathematics Mathematics Dirichlet problem Mean curvature Computer Science::Information Retrieval 010102 general mathematics Riemannian manifold MEAN-CURVATURE Differential Geometry (math.DG) Harmonic function [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] Bounded function Graph equation MANIFOLDS Mean curvature equation ASYMPTOTIC DIRICHLET PROBLEM Mathematics::Differential Geometry [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG] p-Laplace equation |
| Popis: | We prove that every entire solution of the minimal graph equation that is bounded from below and has at most linear growth must be constant on a complete Riemannian manifold $M$ with only one end if $M$ has asymptotically non-negative sectional curvature. On the other hand, we prove the existence of bounded non-constant minimal graphic and $p$-harmonic functions on rotationally symmetric Cartan-Hadamard manifolds under optimal assumptions on the sectional curvatures. The authors are grateful to Professor Luciano Mari who pointed out an error in the proof of the previous version of Proposition 3.1 To appear in Proc. Roy. Soc. Edinburgh Sect. A |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|