On non-homeomorphic surfaces with close DN maps
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_*
Fields of Study & Subjects
Numerical methods in inverse problems
Spectral Theory in Mathematical Physics
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 29 January 2026
- Language
- EN
- Document type
- Preprint