Reference : A Polyakov formula for sectors
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Physical, chemical, mathematical & earth Sciences : Mathematics
A Polyakov formula for sectors
Aldana Dominguez, Clara Lucia mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Rowlett, Julie []
Submitted version
[en] polyakov formula ; zeta-regularized determinant ; sectors ; conical singularities ; angular variation
[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.
Mathematics Research Unit
Fonds National de la Recherche - FnR
Researchers ; Professionals
FnR ; 7926179

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VPSectors-SV.pdfPublished in the mathematical arxivAuthor preprint385.56 kBView/Open

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