PDE Seminar Abstracts

# Ricci flow and the determinant of the Laplacian on non-compact surfaces

Frédéric Rochon
Australian National University
28 Mar 2011 2-3pm, Mills Lecture Room 202

## Abstract

After introducing the notion of determinant of the Laplacian on a non-compact surface with ends asymptotically isometric to a cusp or a funnel, we will show that in a given conformal class (with ’renormalized area’ fixed), this determinant is maximal for the metric of constant scalar curvature, generalizing a well-known result of Osgood, Phillips and Sarnak in the compact case. This will be achieved by combining a corresponding Polyakov formula with some long time existence result for the Ricci flow for such metrics. This is a joint work with P. Albin and C.L. Aldana.