Albin, PierreAldana, ClaraRochon, Frederic2015-12-130360-5302http://hdl.handle.net/1885/71636On 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.Keywords: Determinant of the Laplacian; Polyakov formula; Renormalized traces; Ricci flow; Uniformization of noncompact surfaces201310.1080/03605302.2012.7218532016-02-24