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Determinant of the Laplacian on Tori of Constant Positive Curvature with one Conical Point

Part of: Partial differential equations on manifolds; differential operators General theory of linear operators Riemann surfaces

Published online by Cambridge University Press:  04 January 2019

Victor Kalvin  and
Alexey Kokotov
Victor Kalvin
Affiliation:
Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8 Email: [email protected]@concordia.ca
Alexey Kokotov
Affiliation:
Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8 Email: [email protected]@concordia.ca
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Abstract

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We find an explicit expression for the zeta-regularized determinant of (the Friedrichs extensions of) the Laplacians on a compact Riemann surface of genus one with conformal metric of curvature $1$ having a single conical singularity of angle $4\unicode[STIX]{x1D70B}$.

Keywords

determinant of Laplacianmoduli spacespectral zeta-functioncurvature oneconical pointconical singularityRiemann surfacecompact Riemann surface

MSC classification

Primary: 47A10: Spectrum, resolvent
Secondary: 58J52: Determinants and determinant bundles, analytic torsion 30F45: Conformal metrics (hyperbolic, Poincaré, distance functions)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 2 , June 2019 , pp. 341 - 347
Copyright
© Canadian Mathematical Society 2018 

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