Work

A Polyakov Formula for Sectors

Year: 2017

Type: article

Abstract: 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 origin. We compute explicitly all the contributions to this formula coming from the different parts of the sector. In the process, we obtain an explicit expression for the heat kernel on an infinite area sector using Carslaw-Sommerfeld's heat kernel. We also compute the zeta-regularized determinant of rectangular domains of unit area and prove that it is uniquely maximized by the square.

Source: Journal of Geometric Analysis

DOI: 10.1007/s12220-017-9888-y

Authors: Clara L. Aldana, Julie Rowlett

Institutions: University of Luxembourg, Chalmers University of Technology, University of Gothenburg

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Agence Nationale de la Recherche, Fonds National de la Recherche Luxembourg