Ricci Flow and the Determinant of the Laplacian on Non-Compact Surfaces

Pierre Albin*, Clara L. Aldana, Frédéric Rochon

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    14 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)711-749
    Number of pages39
    JournalCommunications in Partial Differential Equations
    Volume38
    Issue number4
    DOIs
    Publication statusPublished - Apr 2013

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