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A Polyakov formula for sectors
Aldana Dominguez, Clara Lucia; Rowlett, Julie


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Keywords :
polyakov formula; zeta-regularized determinant; sectors; conical singularities; angular variation
Abstract :
[en] We consider finite area convex Euclidean circular sectors. We prove a variational Polyakov formula which shows how the zeta-regularized determinant of the Laplacian varies with respect to the opening angle. Varying the angle corresponds to a conformal deformation in the direction of a conformal factor with a logarithmic singularity at the corner. As an application of the method, we obtain an analogues Polyakov formula for a surface with one conical singularity. We compute the zeta-regularized determinant of rectangular domains of fixed area and prove that it is uniquely maximized by the square.
Research center :
Mathematics Research Unit
Disciplines :
Author, co-author :
Aldana Dominguez, Clara Lucia ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Rowlett, Julie
Language :
Title :
A Polyakov formula for sectors
Publication date :
21 September 2015
Version :
Submitted version
Number of pages :
FnR Project :
FNR7926179 - Spectral Invariants On Manifolds With Geometric Singularities, 2014 (15/01/2015-15/12/2017) - Clara Lucia Aldana Dominguez
Name of the research project :
Funders :
FNR - Fonds National de la Recherche [LU]
Available on ORBilu :
since 25 November 2015


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