Jenkins-Serrin graphs in $M\times\mathbb{R}$
Differential Geometry
2021-07-13 v4
Abstract
The so called Jenkins-Serrin problem is a kind of Dirichlet problem for graphs with prescribed mean curvature that combines, at the same time, continuous boundary data with regions of the boundary where the boundary values explodes either to or to We give a survey on the development of Jenkins-Serrin type problems over domains on Riemannian manifolds. The existence of this type of graphs imposes restrictions on the geometry of the boundary of these domains. We also improve some earlier results by proving Theorem 1.8, and prove the existence of translating Jenkins-Serrin graphs (Theorem 1.9).
Keywords
Cite
@article{arxiv.1806.02414,
title = {Jenkins-Serrin graphs in $M\times\mathbb{R}$},
author = {Eddygledson S. Gama and Esko Heinonen and Jorge H. de Lira and Francisco Martin},
journal= {arXiv preprint arXiv:1806.02414},
year = {2021}
}
Comments
Revised version. To appear in the proceedings of the "M:IV winter workshop 2018" held at the University of Granada, January 9-12, 2018