Determinant of Friederichs Dirichlet Laplacians on $2$-dimensional hyperbolic cones

Abstract

We explicitly express the spectral determinant of Friederichs Dirichlet Laplacians on the 2-dimensional hyperbolic (Gaussian curvature -1) cones in terms of the cone angle and the geodesic radius of the boundary. The related results in the recent paper "Riemann-Roch isometries in the non-compact orbifold setting," J. Eur. Math. Soc. 22 (2020) by G. Freixas i Montplet and A. von Pippich turn out to be incorrect.

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Cited by in corpus (3)

• Classical Liouville Action and Uniformization of Orbifold Riemann Surfaces
• Determinants of Laplacians for constant curvature metrics with three conical singularities on 2-sphere
• The variation of Barnes and Bessel zeta functions