Dmitrii Korikov

collaborators

5 papers

math-ph2025

On perturbations of the DN map of a disk causing changes of surface topology

Dmitrii Korikov

We establish the degeneration of the Schottky double of a genus 1 Riemann surface with boundary as its DN map tends to the DN map of the unit disk.

math.DG2025

Variational formulas for determinant of Laplacian on higher genus polyhedral surface

Dmitrii Korikov, Alexey Kokotov

Let $X$ be a Riemann surface of genus $g \geq 1$ endowed with a flat conical metric $m$ and let $det Δ$ be the $ζ$ -regularized determinant of the Friedrichs Laplacian on $(X,m…

math.SP2025

On an infinitesimal Polyakov formula for genus zero polyhedra

Alexey Kokotov, Dmitrii Korikov

Let $X$ be a genus zero compact polyhedral surface (the Riemann sphere equipped with a flat conical metric $m$ ). We derive the variational formulas for the determinant of the Lapla…

math.SP2025

On a polygon version of Wiegmann-Zabrodin formula

Alexey Kokotov, Dmitrii Korikov

Let $P$ be a convex polygon in $C$ and let $Δ_{D, P}$ be the operator of the Dirichlet boundary value problem for the Lapalcian $Δ = - 4 \partial_{z} \partial_{z ˉ}$ in $P$ .…

math-ph2025

Determination of period matrix of double of surface with boundary via its DN map

Dmitrii Korikov

As is well-known, a conformal class of a surface $M$ with boundary $Γ$ is determined by its DN map $Λ$ . In the paper, the algorithm for determination of the $b$ -period matrix $\mat…