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arXiv · 0909.0807

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

Pierre Albin·Clara L. Aldana·Frédéric Rochon
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Abstract

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.

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Pierre Albin, Clara L. Aldana, Frédéric Rochon. 2013-03-31. Ricci flow and the determinant of the Laplacian on non-compact surfaces. https://doi.org/10.1080/03605302.2012.721853

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