42 research outputs found
Propagation of boundary CR foliations and Morera type theorems for manifolds with attached analytic discs
We prove that generic homologically nontrivial -parameter family of
analytic discs attached by their boundaries to a CR manifold in
tests CR functions: if a smooth function on
extends analytically inside each analytic disc then it satisfies the tangential
CR equations.
In particular, we answer, in real analytic category, two open questions: on
characterization of analytic functions in planar domains (the strip-problem),
and on characterization of boundary values of holomorphic functions in domains
in (a conjecture of Globevnik and Stout). We also characterize
complex curves in as real 2-manifolds admitiing homologically
nontrivial 1-parameter families of attached analytic discs.
The proofs are based on reduction to a problem of propagation of degeneracy
of CR foliations of torus-like manifolds.Comment: The version accepted in Advances in Mathematic