Abstract: 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 manifo...
(read more)
Topics: 
Mathematical analysis
Pure mathematics
Combinatorics