%0 Journal Article
%T Ricci flow and the determinant of the Laplacian on non-compact surfaces
%A Pierre Albin
%A Clara L. Aldana
%A Fr¨¦d¨¦ric Rochon
%J Mathematics
%D 2009
%I arXiv
%R 10.1080/03605302.2012.721853
%X On compact surfaces with or without boundary, Osgood, Phillips and Sarnak proved that the maximum of the determinant of the Laplacian within a conformal class of metrics with fixed area occurs at a metric of constant curvature and, for negative Euler characteristic, exhibited a flow from a given metric to a constant curvature metric along which the determinant increases. The aim of this paper is to perform a similar analysis for the determinant of the Laplacian on a non-compact surface whose ends are asymptotic to hyperbolic funnels or cusps. In that context, we show that the Ricci flow converges to a metric of constant curvature and that the determinant increases along this flow.
%U http://arxiv.org/abs/0909.0807v3