Pseudoholomorphic discs near an elliptic point
We prove the existence and study the geometry of Bishop discs near an elliptic point of a real n-dimensional submanifold of an almost complex n-dimensional manifold.
math.CV↗
arXiv subjects
Alexandre Sukhov
Publications and source records attributed to Alexandre Sukhov.
An existence theorem for stationary discs in almost complex manifolds
An existence theorem for stationary discs of strongly pseudoconvex domains in almost complex manifolds is proved. More precisely, it is shown that, for all points of a suitable neighborhood of the boundary and for any vector belonging to certain open subsets of the tangent spaces there exists a unique stationary disc passing through that point and tangent to the given vector.
math.CV↗
Fefferman's mapping theorem on almost complex manifolds
We give a necessary and sufficient condition for the smooth extension of a diffeomorphism between smooth strictly pseudoconvex domains in four real dimensional almost complex manifolds. The proof is mainly based on a reflection principle for pseudoholomorphic discs, on precise estimates of the Kobayashi-Royden infinitesimal pseudometric and on the scaling method in almost complex manifolds.
math.CV↗
Segre varieties and Lie symmetries
Using the classical S.Lie method we obtain a complete description of infinitesimal symmetries of a holomorphic PDE system defining the Segre family of a real analytic hypersurface. This gives a new proof of some well known results of CR geometry.
math.CV↗
Segre varieties, CR geometry and Lie symmetries of second order PDE systems
We show that biholomorphic automorphisms of a real analytic CR manifold can be considered as (pointwise) Lie symmetries of a holomorphic second order PDE system defining its Segre family. This allows to use general methods of the geometric PDE theory in order to study the CR geometry of real analytic manifolds.
math.CV↗