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Polyakov-Alvarez Formula for Curvilinear Polygonal Domains with Slits

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arxiv 2501.07682 v1 pith:FSC76LYK submitted 2025-01-13 math-ph math.DGmath.MPmath.SP

Ellen Krusell This is my paper
classification math-phmath.DGmath.MPmath.SP
keywords domainscurvilineardeterminantformulapolyakov-alvarezpolygonalregularizedzeta
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abstract

We consider the $\zeta$-regularized determinant of the Friedrichs extension of the Dirichlet Laplace-Beltrami operator on curvilinear polygonal domains with corners of arbitrary positive angles. In particular, this includes slit domains. We obtain a short time asymptotic expansion of the heat trace using a classical patchwork method. This allows us to define the $\zeta$-regularized determinant of the Laplacian and prove a comparison formula of Polyakov-Alvarez type for a smooth and conformal change of metric.

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  1. Anticyclotomic diagonal classes and Beilinson--Flach elements

    math.NT 2025-09 conditional novelty 6.0 of 10

    Anticyclotomic diagonal cycle classes are shown to match Beilinson-Flach elements up to explicit factors for a CM weight-one Eisenstein degeneration.

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