The geometric Neumann problem for the Liouville equation
Analysis of PDEs
2015-03-19 v1 Differential Geometry
Abstract
In this paper we classify the solutions to the geometric Neumann problem for the Liouville equation in the upper half-plane or an upper half-disk, with the energy condition given by finite area. As a result, we classify the conformal Riemannian metrics of constant curvature and finite area on a half-plane that have a finite number of boundary singularities, not assumed a priori to be conical, and constant geodesic curvature along each boundary arc.
Cite
@article{arxiv.1104.2454,
title = {The geometric Neumann problem for the Liouville equation},
author = {Jose A. Galvez and Asun Jimenez and Pablo Mira},
journal= {arXiv preprint arXiv:1104.2454},
year = {2015}
}