Steklov Institute of Mathematics at St.Petersburg

PREPRINT 22/2002

The Calderon problem for two-dimensional manifolds by the BC-method (a corrected version)

This preprint was accepted December 17, 2002
Contact: M. I. Belishev

ABSTRACT:
 As was shown by M.Lassas and G.Uhlmann (2001), the smooth two-dimensional
compact orientable Riemann manifold with the boundary is uniquely determined
by
its Dirichlet-to-Neumann map up to conformal equivalence. We give a new
proof of this fact based on relations between the Calderon problem and
Function Algebras: 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 from the DN-map by the use of
the Gelfand transform. A simple formula linking the DN-map to the Euler
characteristic of the manifold is derived.