Two-dimensional Calderón problem and flat metrics Full article
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Analysis and Mathematical Physics
ISSN: 1664-2368 , E-ISSN: 1664-235X |
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| Output data | Year: 2025, Volume: 15, Article number : 110, Pages count : 28 DOI: 10.1007/s13324-025-01112-3 | ||
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0006 |
Abstract:
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.
Cite:
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
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
Dates:
| Submitted: | Jan 29, 2025 |
| Accepted: | Jul 17, 2025 |
| Published print: | Jul 24, 2025 |
| Published online: | Jul 24, 2025 |
Identifiers:
| Web of science: | WOS:001534744100001 |
| Scopus: | 2-s2.0-105011398327 |
| OpenAlex: | W4412935833 |
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