Comment on the preprint arXiv:2501.17471 "Two-dimensional Calderon Problem and Flat Metrics" by V.A.Sharafutdinov

TL;DR

This paper critically examines a preprint claiming to determine Riemann surfaces from Dirichlet-to-Neumann maps, raising questions about the validity of key results in the original work.

Contribution

The paper provides a detailed critique of the proof and claims in Sharafutdinov's preprint regarding the inverse problem for Riemann surfaces.

Findings

Raises concerns about the validity of Theorem 1.1

Highlights potential gaps in the original proof

Questions the general applicability of the main results

Abstract

The notice provides some critical remarks on a paper (preprint) by V.A.Sharafutdinov. The remarks mainly concern Theorem 1.1 on determination of the Riemann surface from its Dirichlet-to-Neuman map, which is declared as one of the basic results of the paper.