Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New extension phenomena for solutions of tangential Cauchy\,-\,Riemann
  Equations   In our recent work [25] we showed that $C^\infty$ CR-diffeomorphisms of
real-analytic Levi-nonflat hypersurfaces in $\mathbb C^{2}$ are not analytic in
general. This result raised again the question on the nature of CR-maps of
real-analytic hypersurfaces.
  In this paper, we give a complete picture of what CR-maps actually are.
First, we discover an analytic continuation phenomenon for CR-diffeomorphisms
which we call the {\em sectorial analyticity property}. It appears to be the
optimal regularity property for CR-diffeomorphisms in general. We emphasize
that such type of extension never appeared previously in the literature.
Second, we introduce the class of {\em Fuchsian type hypersurfaces} and prove
that (infinitesimal generators of) CR-automorphisms of a Fuchsian type
hypersurface are still analytic. In particular, this solves a problem
formulated in [28].
  Finally, we prove a regularity result for {\em formal} CR-automorphisms of
Fuchsian type hypersurfaces.

11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg