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Journal Article

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

##### Locator

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##### Fulltext (public)

0909.0807

(Preprint), 418KB

03605302.2012.pdf

(Any fulltext), 387KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

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.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000E-7CC1-2

##### 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.