Реферат: For a compact Riemannian manifold (M, g) with boundary ∂M, the Dirichlet-to-Neumann operator g : C∞(∂M) −→ C∞(∂M) is defined by g f = ∂u ∂ν ∂M, where ν is the unit outer normal vector to the boundary and u is the solution to the Dirichlet problem gu = 0, u|∂M = f . Let g∂ be the Riemannian metric on ∂M induced by g. The Calderón problem is posed as follows: To what extent is (M, g) determined by the data (∂M, g∂, g)? We prove the uniqueness theorem: A compact connected two-dimensional Riemannian manifold (M, g) with non-empty boundary is determined by the data (∂M, g∂, g) uniquely up to conformal equivalence.

Библиографическая ссылка: Sharafutdinov V.A.
Two-dimensional Calderón problem and flat metrics
Analysis and Mathematical Physics. 2025. V.15. 110 :1-28. DOI: 10.1007/s13324-025-01112-3 WOS Scopus OpenAlex

Даты:

Поступила в редакцию:	29 янв. 2025 г.
Принята к публикации:	17 июл. 2025 г.
Опубликована в печати:	24 июл. 2025 г.
Опубликована online:	24 июл. 2025 г.

Идентификаторы БД:

Web of science:	WOS:001534744100001
Scopus:	2-s2.0-105011398327
OpenAlex:	W4412935833

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