Steklov Institute of Mathematics at St.Petersburg

PREPRINT 10/2002

The Calderon problem for two-dimensional manifolds by the BC-method

This preprint was accepted June 10, 2002
Contact: M.I.Belishev

ABSTRACT:
We show that smooth two-dimensional compact orientable Riemann
manifold with border is determined by
its Dirichlet-to-Neumann map up to conformal equivalence. The
manifold is identified with the spectrum of the algebra of
holomorphic functions determined by the DN-map up to isometry;
as such, the manifold is recovered through the DN-map by the Gelfand
transform.