Dmitrii Korikov

Preprint Aug 2026

The determinant of the Dirichlet-to-Neumann map for a surface with boundary and periods of holomorphic differentials on its double

Let $(M,g)$ be a smooth orientable $2d$ Riemannian manifold of genus $\mathfrak{g}$ with Riemannian metric $g$ and connected boundary $\Gamma$. Let $\Lambda$ be the Dirichlet-to-Neumann map on $\Gamma$ and let ${\rm det}_\zeta(\Lambda)$ be its (modified, i. e. with zero mode excluded) $\zeta$-regularized determinant. I...

Dmitrii Korikov, Alexey Kokotov · 1 citation

Preprint Aug 2026

On the Dirichlet-to-Neumann conformal invariant of bounded planar domains

Using an analogue of Mandelstam-Giddings-Wolpert diagrams, we introduce a new canonical representative of the conformal class of a bounded domain of arbitrary connectivity in $\mathbb{C}$ as a flat conical surface with geodesic boundary (a"truncated light-cone diagram", simply LC-diagram in the sequel). The space of th...

Alexey Kokotov, Dmitrii Korikov, M. Nenasheva · 0 citations

Preprint Aug 2026

The determinant of the Dirichlet-to-Neumann map for a surface with boundary and periods of holomorphic differentials on its double

Let $(M,g)$ be a smooth orientable $2d$ Riemannian manifold of genus $\mathfrak{g}$ with Riemannian metric $g$ and connected boundary $\Gamma$. Let $\Lambda$ be the Dirichlet-to-Neumann map on $\Gamma$ and let ${\rm det}_\zeta(\Lambda)$ be its (modified, i. e. with zero mode excluded) $\zeta$-regularized determinant. I...

Dmitrii Korikov, Alexey Kokotov · 1 citation