Browsing by Author "ZAITSEV, DMITRI"
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Actions of groups of birationally extendible automorphisms
ZAITSEV, DMITRI (World Science Publishing, 1996)The origin of this work is found in the study of automorphisms of domains D in Cn, n > 1. For example, suppose for the moment that D is relatively compact and recall that in this case the group Aut(D) of all holomorphic ... 
Approximation and convergence of formal CRmappings
ZAITSEV, DMITRI (Oxford University Press, 2003)Let M ? CN be a minimal realanalytic CRsubmanifold and M? ? CN? a realalgebraic subset through points p ? M and p? ? M?. We show that that any formal (holomorphic) mapping f : (CN, p) ? (CN? , p?), sending M into M?, ... 
Boundary jets of holomorphic maps between strongly pseudoconvex domains
ZAITSEV, DMITRI (Elsevier, 2008)We study jets of germs of holomorphic maps between two strongly pseudoconvex domains under the condition that the image of one domain is contained into the other and a given boundary point is (nontangentially) mapped to ... 
Boundary problem for levi flat graphs
ZAITSEV, DMITRI (2011) 
A BurnsKrantz type theorem for domains with corners
ZAITSEV, DMITRI (Springer, 2006)The goal of this paper is twofold. First, to give purely local boundary uniqueness results for maps defined only on one side as germs at a boundary point and hence not necessarily sending any domain to itself and also under ... 
A CauchyKowalevsky theorem for overdetermined systems of nonlinear partial differential equations and geometric applications.
ZAITSEV, DMITRI (Taylor & Francis, 2009)The main motivation for the work presented in this paper is to construct real hypersurfaces in Cn+1 with maximal Levi number (see below for the definition), a problem that has been open since Levi numbers were introduced ... 
Deformation of generic submanifolds in a complex manifold
ZAITSEV, DMITRI (Elsevier, 2007)This paper shows that an arbitrary generic submanifold in a complex manifold can be deformed into a 1parameter family of generic submanifolds satisfying strong nondegeneracy conditions. The proofs use a careful analysis ... 
Degenerate real hypersurfaces in C2 with few automorphisms
ZAITSEV, DMITRI (2009)We introduce new biholomorphic invariants for realanalytic hypersurfaces in 2dimensional complex space and show how they can be used to show that a hypersurface possesses few automorphisms. We give conditions, in terms ... 
Domains of polyhedral type and boundary extensions of biholomorphisms
ZAITSEV, DMITRI (1998)For D, D? analytic polyhedra in Cn, it is proven that a biholomorphic mapping f : D ! D? extends holomorphically to a dense boundary subset under certain condition of general position. This result is also extended to ... 
Dynamics of oneresonant biholomorphisms
ZAITSEV, DMITRI (2013)Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in Cn whose differentials have onedimensional family of resonances in the first m eigenvalues, m ? n (but more resonances ... 
Equivalence and embedding problems for CRstructures of any codimension
ZAITSEV, DMITRI (2005) 
The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics
ZAITSEV, DMITRI (Duke University Press, 2005)Our main objective in this paper is to study the class of real hypersurfaces M ? Cn+1 which admit holomorphic (or formal) embeddings into the unit sphere (or, more generally, Levinondegenerate hyperquadrics) in CN+1 ... 
Equivalences of real submanifolds in complex space.
ZAITSEV, DMITRI (null, International Press, 2001)We show that for any realanalytic submanifold M in CN there is a proper realanalytic subvariety V contained in M such that for any p ? M \ V , any realanalytic submanifold M? in CN, and any p? ? M?, the germs of the ... 
Extension of CRfunctions on wedges.
ZAITSEV, DMITRI (Springer, 2003)The celebrated BoggessPolking theorem [BP82] extending classical results of Lewy [L56] states that all (continuous) CRfunctions on a generic submanifold M in CN extend holomorphically to a wedge in the direction of the ... 
A family of compact strictly pseudoconvex hypersurfaces in C^2 without umbilical points
ZAITSEV, DMITRI; Ebenfelt, Peter; Ngoc Son, Duong (2018)We prove the following: For ϵ>0, let Dϵ be the bounded strictly pseudoconvex domain in ℂ2 given by (logz)2+(logw)2<ϵ2. The boundary Mϵ:=∂Dϵ⊂ℂ2 is a compact strictly pseudoconvex CR manifold without umbilical ... 
Finite jet determination of local analytic CR automorphisms and their parametrization by 2jets in the finite type case.
ZAITSEV, DMITRI (Geometric And Functional Analysis, 2003)We show that germs of local realanalytic CR automorphisms of a realanalytic hypersurface M in C2 at a point p ? M are uniquely determined by their jets of some finite order at p if and only if M is not Leviflat near ... 
Formal and finite order equivalences
ZAITSEV, DMITRI (2011)We show that two families of germs of realanalytic subsets in Cn are formally equivalent if and only if they are equivalent of any finite order. We further apply the same technique to obtain analogous statements for ... 
Holomorphic extension of smooth CRmappings between realanalytic and realalgebraic CRmanifolds
ZAITSEV, DMITRI (International Press, 2003)The classical Schwarz reflection principle states that a continuous map f between realanalytic curves M and M? in C that locally extends holomorphically to one side of M, extends also holomorphically to a neighborhood ...