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

Albin, P., Aldana, C. L., & Rochon, F. (2013). Ricci flow and the determinant of the Laplacian on non-compact surfaces. Communications in partial differential equations, 38 (4): 749, pp. 711. doi:10.1080/03605302.2012.721853.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000E-7CC1-2 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0024-8F33-E
Genre: Journal Article

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0909.0807 (Preprint), 418KB
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 Creators:
Albin, Pierre, Author
Aldana, Clara Lucia1, Author              
Rochon, Frédéric, Author
Affiliations:
1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24012              

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Free keywords: Mathematics, Differential Geometry, math.DG,Mathematics, Analysis of PDEs, math.AP,
 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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 Dates: 2009-09-042009-10-292013
 Publication Status: Published in print
 Pages: 38 pages
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 0909.0807
DOI: 10.1080/03605302.2012.721853
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Title: Communications in partial differential equations
Source Genre: Journal
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Pages: - Volume / Issue: 38 (4) Sequence Number: 749 Start / End Page: 711 - Identifier: -