76 citations · 234 across the 22 of their papers we have counts for
14 papers · 1 filter
A note on the closed range of on q-convex manifolds
Luca Baracco, Alexander Tumanov
We prove that the tangential Cauchy-Riemann operator has closed range on Levi-pseudoconvex CR manifolds that are embedded in a q-convex complex manifold . Our result generalizes…
Stationary discs and finite jet determination for CR mappings in higher codimension
Alexander Tumanov
We discuss stationary discs for generic CR manifolds and apply them to the problem of finite jet determination for CR mappings. We prove that a CR diffeomorphism of two finitely sm…
Pseudoholomorphic discs and symplectic structures in Hilbert space
Alexandre Sukhov, Alexander Tumanov
We develop the theory of -holomorphic discs in Hilbert spaces with almost complex structures. As an aplication, we prove a version of Gromov's symplectic non-squeezing theorem f…
Gluing complex discs to Lagrangian manifolds by Gromov's method
Alexandre Sukhov, Alexander Tumanov
The paper discusses some aspects of Gromov's theory.
Analytic continuation from a family of lines
Alexander Tumanov
Given a function f in the exterior of a convex curve in the real plane, we prove that if the restrictions of f to the tangent lines to the curve extend as entire functions, then th…
Filling real hypersurfaces by pseudoholomorphic discs
Alexandre Sukhov, Alexander Tumanov
We study pseudoholomorphic discs with boundaries attached to a real hypersurface in an almost complex manifold. We give sufficient conditions for filling a one sided neighborhood o…