Ricci flow and the determinant of the Laplacian on non-compact surfaces - Mathematics > Differential GeometryReport as inadecuate




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Abstract: On compact surfaces with or without boundary, Osgood, Phillips and Sarnakproved that the maximum of the determinant of the Laplacian within a conformalclass 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 aconstant curvature metric along which the determinant increases. The aim ofthis paper is to perform a similar analysis for the determinant of theLaplacian on a non-compact surface whose ends are asymptotic to hyperbolicfunnels or cusps. In that context, we show that the Ricci flow converges to ametric of constant curvature and that the determinant increases along thisflow.



Author: Pierre Albin, Clara L. Aldana, Frédéric Rochon

Source: https://arxiv.org/



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