English

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

Spectral Theory 2022-01-12 v1 Mathematical Physics Differential Geometry Functional Analysis math.MP Number Theory

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.

Keywords

Cite

@article{arxiv.2011.05407,
  title  = {Determinant of Friederichs Dirichlet Laplacians on $2$-dimensional hyperbolic cones},
  author = {Victor Kalvin},
  journal= {arXiv preprint arXiv:2011.05407},
  year   = {2022}
}