Optimal stability estimates for determination of a non-orientable surface with boundary via its DN-map

D. V. Korikov

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: As is well-known, a surface with boundary is determined, up to conformal equivalence, by its Dirichlet-to-Neumann (DN) map. In this note, we prove the local estimates of the Teichmüller distance between the conformal classes of non-orientable surfaces $(M,g)$ and $(M',g')$ with given boundary $\Gamma=\partial M=\partial M'$ and the topology via the operator norm of the difference between their DN-maps. These estimates are optimal and they refine the corresponding results of previous works [4, 5].

Key words and phrases: electric impedance tomography of surfaces, Dirichlet-to-Neumann maps, stability of solutions, Teichmüller distance, stability estimates.

UDC: 517.954, 517.98

Received: 15.09.2025