3 citations · 17 across the 20 of their papers we have counts for
24 papers · 1 filter
Strong Ramadanov Conjecture for Real Ellipsoids in : two approaches
Jan Gregorovic, Ilya Kossovskiy, Son-Ying Li +1
In this paper, we provide two (significantly different) proofs of the well known Strong Ramadanov Conjecture for the class of real ellipsoids in the complex -space.
Sphericity and Analyticity of a strictly pdeusoconvex hypersurface in low regularity I
Ilya Kossovskiy, Dmitri Zaitsev
In our earlier work \cite{KZ}, we introduced an analytic regularizability theory for smooth strictly pseudoconvex hypersurfaces in complex space. That is, we found a necessary and…
On the regularity of nondegenerate hypo-analytic structures of hypersurface type
Ilya Kossovskiy, Vinícius Novelli
For a smooth, non-degenerate locally integrable structure of hypersurface type on a manifold , we provide necessary and sufficient conditions for it to be equivalent, near a poi…
Holomorphic vector fields with real integral manifolds
Martin Kolář, Ilya Kossovskiy, Bernhard Lamel
We classify singular holomorphic vector fields in two-dimensional complex space admitting a (Levi-nonflat) real-analytic invariant 3-fold through the singularity. In this way, we c…
The jet transcendence degree of a real hypersurface and Huang-Ji-Yau Conjecture
Jan Gregorovic, Ilya Kossovskiy
We investigate the problem of holomorphic algebraizibility for real hypersurfaces in complex space. We introduce a new invariant of a (real-analytic) Levi-nondegenerate hypersurfac…
New examples of -nondegenerate real hypersurfaces in with arbitrary nilpotent symbols
Martin Kolář, Ilya Kossovskiy, David Sykes
We introduce a class of uniformly -nondegenerate CR hypersurfaces in , for , having a rank Levi kernel. The class is first of all remarkable by the fact t…
Regularity of CR-mappings between Fuchsian type hypersurfaces in
P. Ebenfelt, I. Kossovskiy, B. Lamel
We investigate regularity of CR-mappings between real-analytic infinite type hypersurfaces in . We show that, under the Fuchsian type condition, all (respectively form…
Classification of homogeneous strictly pseudoconvex hypersurfaces in
Ilya Kossovskiy, Alexander Loboda
Locally homogeneous strictly pseudoconvex hypersurfaces in were classified by E.\,Cartan in 1932. In this work, we complete the classification of locally homogeneous…
Real-analytic coordinates for smooth strictly pseudoconvex CR-structures
Ilya Kossovskiy, Dmitri Zaitsev
For a smooth strictly pseudoconvex hypersurface in a complex manifold, we give a necessary and sufficient condition for being CR-diffeomorphic to a real-analytic CR manifold. Our c…
A complete normal form for everywhere Levi degenerate hypersurfaces in
Martin Kolar, Ilya Kossovskiy
-nondegenerate real hypersurfaces in complex manifolds play an important role in CR-geometry and the theory of Hermitian Symmetric Domains. In this paper, we construct a complet…
The equivalence theory for infinite type hypersurfaces in
Peter Ebenfelt, Ilya Kossovskiy, Bernhard Lamel
We develop a classification theory for real-analytic hypersurfaces in in the case when the hypersurface is of {\em infinite type} at the reference point. This is the…
Equivalence of Cauchy-Riemann manifolds and multisummability theory
Ilya Kossovskiy, Bernhard Lamel, Laurent Stolovitch
We prove that if two real-analytic hypersurfaces in are equivalent formally, then they are also CR-equivalent at the respective point. As a corollary, we p…
Regularity of CR-mappings into Levi-degenerate hypersurfaces
Ilya Kossovskiy, Bernhard Lamel, Ming Xiao
We provide regularity results for CR-maps between real hypersurfaces in complex spaces of different dimension with a Levi-degenerate target. We address both the real-analytic and t…
Normal forms in Cauchy-Riemann Geometry: a survey
Martin Kolar, Ilya Kossovskiy, Dmitri Zaitsev
One of effective ways to solve the equivalence problem and describe moduli spaces for real submanifolds in complex space is the normal form approach. In this survey, we outline som…
Sphericity of a real hypersurface via projective geometry
Ilya Kossovskiy
In this work, we obtain an unexpected geometric characterization of sphericity of a real-analytic Levi-nondegenerate hypersurface . We prove that is sphe…
On the embeddability of real hypersurfaces into hyperquadrics
Ilya Kossovskiy, Ming Xiao
In this paper, we provide {\em effective} results on the non-embeddability of real-analytic hypersurfaces into a hyperquadric. We show that, for any , the defining fun…
New extension phenomena for solutions of tangential Cauchy\,-\,Riemann Equations
Ilya Kossovskiy, Bernhard Lamel
In our recent work [25] we showed that CR-diffeomorphisms of real-analytic Levi-nonflat hypersurfaces in are not analytic in general. This result raised…
Convergent normal form and canonical connection for hypersurfaces of finite type in
Ilya Kossovskiy, Dmitri Zaitsev
We study the holomorphic equivalence problem for finite type hypersurfaces in . We discover a geometric condition, which is sufficient for the existence of a natural c…
On the analyticity of CR-diffeomorphisms
Ilya Kossovskiy, Bernhard Lamel
In any positive CR-dimension and CR-codimension we provide a construction of real-analytic holomorphically nondegenerate CR-submanifolds, which are CR-equivalent, but ar…
Convergent normal form for real hypersurfaces at generic Levi degeneracy
Ilya Kossovskiy, Dmitri Zaitsev
We construct a complete convergent normal form for a real hypersurface in $\CC{N},\,N\geq 2$ at generic Levi degeneracy. This seems to be the first convergent normal form for a Lev…
Analytic Differential Equations and Spherical Real Hypersurfaces
Ilya Kossovskiy, Rasul Shafikov
We establish an injective correspondence between real-analytic nonminimal hypersurfaces , spherical at a generic point, and…
Analytic Continuation of Holomorphic Mappings From Non-minimal Hypersurfaces
I. Kossovskiy, R. Shafikov
We study the analytic continuation problem for a germ of a biholomorphic mapping from a non-minimal real hypersurface $M\subset\CC{n}$ into a real hyperquadric $\mathcal Q\subset\C…
Classification of homogeneous CR-manifolds in dimension 4
V. K. Beloshapka, I. G. Kossovskiy
Locally homogeneous CR-manifolds in dimension 3 were classified, up to local CR-equivalence, by E.Cartan. We classify, up to local CR-equivalence, all locally homogeneous CR-manifo…
Continuation of CR-Automorphisms of Levi Degenerate Hyperquadrics to the Projective Space
A. V. Isaev, I. G. Kossovskiy
We show that every CR-automorphism of the closure of a Levi degenerate hyperquadric in the projective space extends to a holomorphic automorphism of the projective space.