Asymptotic Dirichlet problems in warped products
| Autor: | Esko Heinonen, Jorge H. de Lira, Jean-Baptiste Casteras, Ilkka Holopainen |
|---|---|
| Přispěvatelé: | Geometric Analysis and Partial Differential Equations, Department of Mathematics and Statistics |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics MEAN-CURVATURE EQUATION Geodesic General Mathematics Boundary (topology) Killing graph 01 natural sciences Dirichlet distribution Killing vector field symbols.namesake 0103 physical sciences FOS: Mathematics 111 Mathematics INFINITY Hadamard manifold 0101 mathematics warped product Mathematics Dirichlet problem Mean curvature 010102 general mathematics 16. Peace & justice Mathématiques KILLING GRAPHS Differential Geometry (math.DG) Product (mathematics) MANIFOLDS symbols Mean curvature equation 010307 mathematical physics Mathematics::Differential Geometry 58J32 53C21 |
| Zdroj: | Mathematische Zeitschrift |
| Popis: | We study the asymptotic Dirichlet problem for Killing graphs with prescribed mean curvature H in warped product manifolds M× ϱR. In the first part of the paper, we prove the existence of Killing graphs with prescribed boundary on geodesic balls under suitable assumptions on H and the mean curvature of the Killing cylinders over geodesic spheres. In the process we obtain a uniform interior gradient estimate improving previous results by Dajczer and de Lira. In the second part we solve the asymptotic Dirichlet problem in a large class of manifolds whose sectional curvatures are allowed to go to 0 or to - ∞ provided that H satisfies certain bounds with respect to the sectional curvatures of M and the norm of the Killing vector field. Finally we obtain non-existence results if the prescribed mean curvature function H grows too fast. SCOPUS: ar.j info:eu-repo/semantics/published |
| Databáze: | OpenAIRE |
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