• Corpus ID: 203610175

Polyakov-Alvarez type comparison formulas for determinants of Laplacians on Riemann surfaces with conical metrics

@article{Kalvin2019PolyakovAlvarezTC,
  title={Polyakov-Alvarez type comparison formulas for determinants of Laplacians on Riemann surfaces with conical metrics},
  author={Victor Kalvin},
  journal={arXiv: Mathematical Physics},
  year={2019}
}
  • Victor Kalvin
  • Published 30 September 2019
  • Mathematics
  • arXiv: Mathematical Physics
We prove Polyakov-Alvarez type comparison formulas for the determinants of Friederichs selfadjoint extensions of Laplacians corresponding to conformally equivalent conical metrics on compact Riemann surfaces. We illustrate our results by obtaining new and recovering known explicit formulas for determinants of Laplacians on surfaces with conical singularities. 

Figures from this paper

Determinant of Friedrichs Dirichlet Laplacians on 2-dimensional hyperbolic cones

  • Victor Kalvin
  • Mathematics
    Communications in Contemporary Mathematics
  • 2021
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

Polyakov formulas for conical singularities in two dimensions

We investigate the zeta-regularized determinant and its variation in the presence of conical singularities, boundaries, and corners. For surfaces with isolated conical singularities which may also

Spanning trees, cycle-rooted spanning forests on discretizations of flat surfaces and analytic torsion

We study the asymptotic expansion of the determinant of the graph Laplacian associated to discretizations of a tileable surface endowed with a flat unitary vector bundle. By doing so, over the

Spectral Determinant on Euclidean Isosceles Triangle Envelopes

We study extremal properties of the determinant of Friedrichs selfadjoint Laplacian on the Euclidean isosceles triangle envelopes of fixed area as a function of angles. We deduce an explicit closed

References

SHOWING 1-10 OF 46 REFERENCES

Conformal invariants for determinants of laplacians on Riemann surfaces

For a Riemann surface with smooth boundaries, conformal (Weyl) invariant quantities proportional to the determinant of the scalar Laplacian operator are constructed both for Dirichlet and Neumann

Tau-functions on spaces of Abelian differentials and higher genus generalizations of Ray-Singer formula

Let $w$ be an Abelian differential on compact Riemann surface of genus $g\geq 1$. We obtain an explicit holomorphic factorization formula for $\zeta$-regularized determinant of the Laplacian in flat

Prescribing curvature on compact surfaces with conical singularities

We study the Berger-Nirenberg problem on surfaces with conical singularities, i.e, we discuss conditions under which a function on a Riemann surface is the Gaussian curvature of some conformal metric

Lowest Landau level on a cone and zeta determinants

We consider the integer QH state on Riemann surfaces with conical singularities, with the main objective of detecting the effect of the gravitational anomaly directly from the form of the wave

Precise Constants in Bosonization Formulas on Riemann Surfaces. I

A computation of the constant appearing in the spin-1 bosonization formula is given. This constant relates Faltings’ delta invariant to the zeta-regularized determinant of the Laplace operator with

Coordonnées polaires sur les surfaces riemanniennes singulières

We study conditions under which a point of a Riemannian surface has a neighborhood that can be parametrized by polar coordinates. The point under investigation can be a regular point or a conical

Asymptotic expansions of double zeta-functions of Barnes, of Shintani, and Eisenstein series

Abstract The present paper contains three main results. The first is asymptotic expansions of Barnes double zeta-functions, and as a corollary, asymptotic expansions of holomorphic Eisenstein series

Burghelea-Friedlander-Kappeler's gluing formula for the zeta-determinant and its applications to the adiabatic decompositions of the zeta-determinant and the analytic torsion

The gluing formula of the zeta-determinant of a Laplacian given by Burghelea, Friedlander and Kappeler contains an unknown constant. In this paper we compute this constant to complete the formula