Solvability of Minimal Graph Equation Under Pointwise Pinching Condition for Sectional Curvatures
| Autor: | Jean-Baptiste Casteras, Ilkka Holopainen, Esko Heinonen |
|---|---|
| Přispěvatelé: | Department of Mathematics and Statistics, Quantitative methods for stochastic models in physics (MEPHYSTO), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université libre de Bruxelles (ULB), Département de Mathématique [Bruxelles] (ULB), Faculté des Sciences [Bruxelles] (ULB), Université libre de Bruxelles (ULB)-Université libre de Bruxelles (ULB), Helsingin yliopisto = Helsingfors universitet = University of Helsinki, Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Inria Lille - Nord Europe, University of Helsinki, Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université libre de Bruxelles (ULB)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Mathematics - Differential Geometry
ASYMPTOTIC DIRICHLET PROBLEMS RIEMANNIAN-MANIFOLDS X R HADAMARD MANIFOLDS Minimal graph equation 01 natural sciences Upper and lower bounds HARMONIC DIFFEOMORPHISMS Combinatorics 0103 physical sciences FOS: Mathematics 111 Mathematics INFINITY NONSOLVABILITY Hadamard manifold HYPERBOLIC SPACE Nabla symbol 0101 mathematics [MATH]Mathematics [math] CONSTANT MEAN-CURVATURE ComputingMilieux_MISCELLANEOUS Mathematics Dirichlet problem Pointwise 010308 nuclear & particles physics Hyperbolic space 010102 general mathematics KILLING GRAPHS Compact space Differential Geometry (math.DG) Graph equation Geometry and Topology 58J32 53C21 |
| Zdroj: | Journal of Geometric Analysis Journal of Geometric Analysis, 2016, ⟨10.1007/s12220-016-9712-0⟩ |
| DOI: | 10.1007/s12220-016-9712-0⟩ |
| Popis: | We study the asymptotic Dirichlet problem for the minimal graph equation on a Cartan-Hadamard manifold $M$ whose radial sectional curvatures outside a compact set satisfy an upper bound $$K(P)\le - \frac{\phi(\phi-1)}{r(x)^2}$$ and a pointwise pinching condition $$|K(P)|\le C_K|K(P')|$$ for some constants $\phi>1$ and $C_K\ge 1$, where $P$ and $P'$ are any 2-dimensional subspaces of $T_xM$ containing the (radial) vector $\nabla r(x)$ and $r(x)=d(o,x)$ is the distance to a fixed point $o\in M$. We solve the asymptotic Dirichlet problem with any continuous boundary data for dimensions $n>4/\phi+1$. Comment: To appear in J. Geom. Anal |
| Databáze: | OpenAIRE |
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