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arXiv · 1104.2454

The geometric Neumann problem for the Liouville equation

Jose A. Galvez·Asun Jimenez·Pablo Mira
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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.

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Jose A. Galvez, Asun Jimenez, Pablo Mira. 2011-04-13. The geometric Neumann problem for the Liouville equation. https://arxiv.org/abs/1104.2454

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