On non-homeomorphic surfaces with close DN maps
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913100493488128 |
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| author | Korikov, D. V. |
| author_facet | Korikov, D. V. |
| contents | 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 $Γ$: $$\|Λ-Λ_*\|_{B(H^{1/2}(Γ);H^{-1/2}(Γ))}\to 0\,\Longrightarrow \ Sys(2M)\to 0.$$ |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_13236 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On non-homeomorphic surfaces with close DN maps Korikov, D. V. Complex Variables Mathematical Physics Primary: 35R30, 46J20, Secondary: 46J15, 30F15 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 $Γ$: $$\|Λ-Λ_*\|_{B(H^{1/2}(Γ);H^{-1/2}(Γ))}\to 0\,\Longrightarrow \ Sys(2M)\to 0.$$ |
| title | On non-homeomorphic surfaces with close DN maps |
| topic | Complex Variables Mathematical Physics Primary: 35R30, 46J20, Secondary: 46J15, 30F15 |
| url | https://arxiv.org/abs/2602.13236 |