13 citations · 54 across the 19 of their papers we have counts for
20 papers
Spectral determinants of flat metrics on the bielliptic genus-two locus
Victor Kalvin
We obtain a closed explicit formula for the spectral determinant of flat conical metrics on the bielliptic genus-two locus. The metrics are generated by holomorphic one-forms with…
Spectral determinants of the Bolza surface and the Klein quartic
Victor Kalvin
We obtain closed explicit formulas for the spectral determinants of the smooth hyperbolic Bolza surface and the Klein quartic. In each case, a multiplicative relation expresses the…
Corner contributions to Neumann jump determinants: three model calculations and a BFK conjecture
Victor Kalvin
We formulate a local corner-factor conjecture for the determinant of the Neumann jump operator on a piecewise real-analytic cutting curve. For the mirror double of a simply connect…
Triangulations of singular constant curvature spheres via Belyi functions and determinants of Laplacians
Victor Kalvin
We study the zeta-regularized spectral determinant of the Friedrichs Laplacians on the singular spheres obtained by cutting and glueing copies of constant curvature (hyperbolic, sp…
Determinants of Laplacians for constant curvature metrics with three conical singularities on 2-sphere
Victor Kalvin
We deduce an explicit closed formula for the zeta-regularized spectral determinant of the Friedrichs Laplacian on the Riemann sphere equipped with arbitrary constant curvature (fla…
Determinant of Friederichs Dirichlet Laplacians on -dimensional hyperbolic cones
Victor Kalvin
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…
Spectral determinant on Euclidean isosceles triangle envelopes of fixed area as a function of angles: absolute minimum and small-angle asymptotics
Victor Kalvin
We study extremal properties of the determinant of Friederichs selfadjoint Laplacian on the Euclidean isosceles triangle envelopes of fixed area as a function of angles. Small-angl…
Polyakov-Alvarez type comparison formulas for determinants of Laplacians on Riemann surfaces with conical singularities
Victor Kalvin
We present and prove Polyakov-Alvarez type comparison formulas for the determinants of Friederichs extensions of Laplacians corresponding to conformally equivalent metrics on a com…
Determinant of Laplacian on tori of constant positive curvature with one conical point
Victor Kalvin, Alexey Kokotov
We find an explicit expression for the zeta-regularized determinant of (the Friedrichs extension) of the Laplacian on a compact Riemann surface of genus one with conformal metric o…
On Determinants of Laplacians on Compact Riemann Surfaces Equipped with Pullbacks of Conical Metrics by Meromorphic Functions
Victor Kalvin
Let be any conical (or smooth) metric of finite volume on the Riemann sphere . On a compact Riemann surface of genus consider a meromorphic funciton…
Metrics of constant positive curvature with conical singularities, Hurwitz spaces, and
Victor Kalvin, Alexey Kokotov
Let be a meromorphic function of degree with simple poles and simple critical points on a compact Riemann surface of genus and let be…
Moduli spaces of meromorphic functions and determinant of Laplacian
Luc Hillairet, Victor Kalvin, Alexey Kokotov
The Hurwitz space is the moduli space of pairs where is a compact Riemann surface and is a meromorphic function on . We study the Laplace operator o…
Spectral Determinants on Mandelstam Diagrams
Luc Hillairet, Victor Kalvin, Alexey Kokotov
We study the regularized determinant of the Laplacian as a functional on the space of Mandelstam diagrams (noncompact translation surfaces glued from finite and semi-infinite cylin…
Analysis of Perfectly Matched Layer operators for acoustic scattering on manifolds with quasicylindrical ends
Victor Kalvin
We prove stability and exponential convergence of the Perfectly Matched Layer (PML) method for acoustic scattering on manifolds with axial analytic quasicylindrical ends. These man…
Limiting absorption principle and perfectly matched layer method for Dirichlet Laplacians in quasi-cylindrical domains
Victor Kalvin
We establish a limiting absorption principle for Dirichlet Laplacians in quasi-cylindrical domains. Outside a bounded set these domains can be transformed onto a semi-cylinder by s…
Exponential Decay of Eigenfunctions and Accumulation of Eigenvalues on Manifolds with Axial Analytic Asymptotically Cylindrical Ends
Victor Kalvin
In this paper we continue our study of the Laplacian on manifolds with axial analytic asymptotically cylindrical ends initiated in~arXiv:1003.2538. By using the complex scaling met…
Aguilar-Balslev-Combes theorem for the Laplacian on a manifold with an axial analytic asymptotically cylindrical end
Victor Kalvin
We develop the complex scaling for a manifold with an asymptotically cylindrical end under an assumption on the analyticity of the metric with respect to the axial coordinate of th…
Complex scaling for the Dirichlet Laplacian in a domain with asymptotically cylindrical end
Victor Kalvin
We develop the complex scaling method for the Dirichlet Laplacian in a domain with asymptotically cylindrical end. We define resonances as discrete eigenvalues of non-selfadjoint o…
Weighted Hardy-Sobolev spaces and complex scaling of differential equations with operator coefficients
Victor Kalvin
In this paper we study weighted Hardy-Sobolev spaces of vector valued functions analytic on double-napped cones of the complex plane. We introduce these spaces as a tool for comple…
Perfectly matched layers for the stationary Schrodinger equation in a periodic structure
Victor Kalvin
We construct a perfectly matched absorbing layer for stationary Schrodinger equation with analytic slowly decaying potential in a periodic structure. We prove the unique solvabilit…