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Isospectrality, comparison formulas for determinants of Laplacian and flat metrics with non-trivial holonomy


Authors: Luc Hillairet and Alexey Kokotov
Journal: Proc. Amer. Math. Soc. 145 (2017), 3915-3928
MSC (2010): Primary 30F30, 30F45, 35P99; Secondary 58J52, 30F10, 32G15
DOI: https://doi.org/10.1090/proc/13494
Published electronically: April 12, 2017
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Abstract: We study comparison formulas for $ \zeta $-regularized determinants of self-adjoint extensions of the Laplacian on flat conical surfaces of genus $ g\geq 2$. The cases of trivial and non-trivial holonomy of the metric turn out to differ significantly.


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Additional Information

Luc Hillairet
Affiliation: MAPMO (UMR 7349 Université d’Orléans-CNRS) UFR Sciences, Bâtiment de mathématiques rue de Chartres, BP 6759 45067 Orléans Cedex 02, France
Email: luc.hillairet@univ-orleans.fr

Alexey Kokotov
Affiliation: Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, Quebec, H3G 1M8 Canada
Email: alexey.kokotov@concordia.ca

DOI: https://doi.org/10.1090/proc/13494
Received by editor(s): November 15, 2015
Received by editor(s) in revised form: September 25, 2016
Published electronically: April 12, 2017
Communicated by: Ken Ono
Article copyright: © Copyright 2017 American Mathematical Society