相关论文: Parametrization of local biholomorphisms of real a…

We consider the problem of describing the local biholomorphic equivalence class of a real-analytic hypersurface $M$ at a distinguished point $p_0\in M$ by giving a normal form for such objects. In order for the normal form to carry useful…

Let f : (M,p)\to (M',p') be a formal biholomorphic mapping between two germs of real analytic hypersurfaces in \C^n, p'=f(p). Assuming the source manifold to be minimal at p, we prove the convergence of the so-called reflection function…

Let H:(M,p)->(M',p') be a formal mapping between two germs of real-analytic generic submanifolds in C^N with nonvanishing Jacobian. Assuming M to be minimal at p and M' holomorphically nondegenerate at p', we prove the convergence of the…

Let M be a connected real-analytic hypersurface in N-dimensional complex euclidean space whose Levi form is nondegenerate at some point. We prove that for every point p in M, there exists an integer k=k(M,p) such that germs at p of local…

A connected real analytic hypersurface M in C^(n+1) whose Levi form is nondegenerate in at least one point - hence at every point of some Zariski-open subset - is locally biholomorphic to the model Heisenberg quadric pseudosphere of…

In this paper, we explore holomorphic Segre preserving maps. First, we investigate holomorphic Segre preserving maps sending the complexification $\mathcal{M}$ of a generic real analytic submanifold $M \subseteq \C^N$ of finite type at some…

In this paper, we study formal mappings between smooth generic submanifolds in multidimensional complex space and establish results on finite determination, convergence and local biholomorphic and algebraic equivalence. Our finite…

Let (M,p) and (M',p') be the germs of real-analytic 1-infinite type hypersurfaces in \C^2. We prove that any formal equivalence sending (M,p) into (M',p') is formally parametrized (and hence uniquely determined by) its jet at p of a…

We show that for any real-analytic submanifold M in C^N there is a proper real-analytic subvariety V contained in M such that for any point p in M\V, any real-analytic submanifold M' in C^N, and any point p' in M', the germs of the…

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 $\mathcal Q\subset\CP{n}$ and prove that under certain non-degeneracy conditions…

Let f : (M,p)\to (M',p') be a formal (holomorphic) nondegenerate map, i.e. with formal holomorphic Jacobian J_f not identically vanishing, between two germs of real analytic generic submanifolds in \C^n, p'=f(p). Assuming the target…

A primary goal in this paper is to study the question that asks when a real analytic submanifold $M$ in ${\mathbb{C}}^{n+1}$ bounds a real analytic (up to $M$) Levi-flat hypersurface $\hat{M}$ near $p\in M$ such that $\hat{M}$ is foliated…

For a smooth, non-degenerate locally integrable structure of hypersurface type on a manifold $M$, we provide necessary and sufficient conditions for it to be equivalent, near a point, to a real-analytic locally integrable structure (the…

We define a new local invariant (called degeneracy) associated to a triple (M,M',H), where M and M' are real submanifolds of C^N and C^N', respectively, and H: M->M' is either a holomorphic map, a formal holomorphic map, or a smooth CR-map.…

For any real-analytic hypersurface M in complex euclidean space of dimension >= 2 which does not contain any complex-analytic subvariety of positive dimension, we show that for every point p in M the local real-analytic CR automorphisms of…

We construct a family of small analytic discs attached to Levi non-degenerate hypersurfaces in $\mathbb{C}^{n+1}$, which is globally biholomorphically invariant. We then apply this technique to study unique determination problems along Levi…

We prove that the local (pseudo)group of biholomorphisms stabilizing a minimal, finitely nondegenerate real algebraic submanifold in C^n is a real algebraic local Lie group (the works of S.M. Baouendi, P. Ebenfelt, L.-P. Rothschild and D.…

We study the local equivalence problem for five dimensional real hypersurfaces $M^5$ of $\mathbb{C}^3$ which are $2$-nondegenerate and of constant Levi rank $1$ under biholomorphisms. We find two invariants, $J$ and $W$, which are expressed…

We prove that if $M$ and $M'$ are algebraic hypersurfaces in $ C^ N$, i.e. both defined by the vanishing of real polynomials, then any sufficiently smooth CR mapping with Jacobian not identically zero extends holomorphically provided the…

We show that every formal embedding sending a real-analytic strongly pseudoconvex hypersurface in $M\subset \C^N$ into another such hypersurface in $M'\subset \C^{N+1}$ is convergent. More generally, if $M$ and $M'$ are merely…