CR-continuation of arc-analytic maps
  Given a set E in a complex space and a point p in E, there is a unique smallest complex-analytic germ containing the germ of E at p, called the holomorphic closure of E at p. We study the holomorphic closure of semialgebraic arc-symmetric sets. Our main application concerns CR-continuation of semialgebraic arc-analytic mappings: A mapping f on a real-analytic CR manifold M which is semialgebraic arc-analytic and CR on a non-empty open subset of M is CR on the whole M. 
Janusz Adamus
math.CV