Asun Jimenez - Universidad de Granada (Espanha)

Resumo: The Liouville equation has a natural geometric Neumann problem attached to it, that comes from de following question: Let U be a domain with smooth boundary. What are the conformal Riemannian metrics on U having constant curvature K, and constant geodesic curvature along each boundary component of the boundary ∂U? We answer this question in two cases: 1. When U is the upper half-plane. We also study the particular case when we impose a certain nite energy condition. As a result, we classify the conformal Riemannian metrics of constant curvature and finite area on a half-plane that have a nite number of boundary singularities, not assumed a priori to be conical, and constant geodesic curvature along each boundary arc. 2. When U is an annulus A. We classify the metrics of constant curvature in A such that each component of is boundary has constant geodesic curvature.

Local: Sala da Pós-Graduação - Bloco 12
Data: Quinta-feira 26/07/2012
Hora: 10:30