Steklov Institute of Mathematics at St.Petersburg

PREPRINT 16/2004

DIRICHLET TO NEUMANN OPERATOR ON DIFFERENTIAL FORMS

This preprint was accepted October 16, 2004

ABSTRACT:
We define the Dirichlet to Neumann operator on exterior
differential forms for a compact Riemannian manifold with boundary
and derive an explicit formula expressing Betti numbers of the
manifold through the DN operator. We express also the
Hilbert transform through the DN map. The Hilbert transform
connects boundary traces of conjugate co-closed forms.
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