The geometric Neumann problem for the Liouville equation

Details The geometric Neumann problem for the Liouville equation The geometric Neumann problem for the Liouville equation

2011-04-13

arxiv.org/abs/1104.2454v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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