Clara L. Aldana
Relative determinants of Laplacians on surfaces with asymptotically cusp ends.
Thu, 01/14/2010 - 16:01 — SomNambulAuthors: Clara L. Aldana
Subjects: Spectral Theory
AbstractWe consider relative determinants of Laplace operators on surfaces with
asymptotically cusp ends. We consider a surface with cusps (M,g) and a metric h
on the surface that is a conformal transformation of the initial metric g. We
prove the existence of the relative determinant of the pair
(\Delta_{h},\Delta_{g}) and other related pairs of operators. We focus on the
decay conditions of the conformal factor at infinity that make it possible to
define the relative determinant.Ricci flow and the determinant of the Laplacian on non-compact surfaces.
Mon, 09/07/2009 - 10:33 — SomNambulAuthors: Pierre Albin, Clara L. Aldana, Frédéric Rochon
Subjects: Differential Geometry
AbstractOn 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.
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