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arXiv · 2602.13236

On non-homeomorphic surfaces with close DN maps

D. V. Korikov
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Abstract

Let $(M,g)$ be a genus $m$ surface with boundary $Γ$ and DN map $Λ$. Introduce the Schottky double $2M$ of $(M,g)$ and denote by $Sys(2M)$ the length of the shortest closed geodesics in the hyperbolic metrics on $2M$. We prove that $Sys(2M)$ is small if $Λ$ is close, in the operator norm, to the DN map $Λ_*$ of some surface $(M_*,g_*)$ of lower genus $m_*<m$ with the same boundary $Γ$: $$\|Λ-Λ_*\|_{B(H^{1/2}(Γ);H^{-1/2}(Γ))}\to 0\,\Longrightarrow \ Sys(2M)\to 0.$$

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D. V. Korikov. 2026-05-07. On non-homeomorphic surfaces with close DN maps. https://arxiv.org/abs/2602.13236

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