相关论文: Stationary discs and finite jet determination for …
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 smooth strictly pseudoconvex Levi generating CR manifolds is…
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 discuss the links between stationary discs, the defect of analytic discs, and 2-jet determination of CR automorphisms of generic nondegenerate real submanifolds of C^N of class C^4.
We prove finite jet determination for (finitely) smooth CR diffeomorphisms of (finitely) smooth Levi degenerate hypersurfaces in $\mathbb{C}^{n+1}$ by constructing generalized stationary discs glued to such hypersurfaces.
The existence of a nondefective stationary disc attached to a nondegenerate model quadric in C^N is a necessary condition to ensure the unique 1-jet determination of the lifts of a key family of stationary discs. In this paper, we give an…
We give an explicit construction of a key family of stationary discs attached to a nondegenerate model quadric in $\mathbb{C}^N$ and derive a necessary condition for which (each lift) of those stationary discs is uniquely determined by its…
We construct a finitely dimensional invariant manifold of holomorphic discs attached to a certain class of smooth pseudconvex hypersurfaces of finite type in $\C^2$, generalizing the notion of stationary discs. The discs we construct are…
We prove finite jet determination results for smooth CR embeddings which are of constant degeneracy, using the method of complete systems. As an application, we derive a reflection principle for mappings between a Levi-nondegenerate…
We obtain an explicit parametrization of stationary discs glued to some Levi non-degenerate hypersurfaces. These discs form a family which is invariant under the action of biholomorphisms. We use this parametrization to construct a local…
We consider a problem whether a CR mapping of a generic manifold in complex space is uniquely determined by its finite jet at a point, which is referred to as finite jet determination. We derive the finite jet determination for CR mappings…
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…
We show that germs of local real-analytic CR automorphisms of a real-analytic hypersurface $M$ in $\C^2$ at a point $p\in M$ are uniquely determined by their jets of some finite order at $p$ if and only if $M$ is not Levi-flat near $p$.…
Let M,M' be smooth real hypersurfaces in N-dimensional space and assume that M is k-nondegenerate at a point p in M. We prove that holomorphic mappings that extend smoothly to M, sending a neighborhood of p in M diffeomorphically into M'…
This paper addresses two questions related to mapping problems. In the first part of the paper, we discuss some recent results regarding the $2$-jet determination for biholomorphisms between smooth (weakly) pseudoconvex hypersurfaces; in…
An intriguing phenomenon regarding Levi-degenerate hypersurfaces is the existence of nontrivial infinitesimal symmetries with vanishing 2-jets at a point. In this work we consider polynomial models of Levi-degenerate real hypersurfaces in…
We compare various definitions of nondegeneracy of the Levi map for real submanifolds of higher codimension in $C^N$ and discuss the generalization to higher codimension of the 2-jet determination for biholomorphisms in the hypersurface…
Germs of locally homogeneous CR manifolds M can be characterized in terms of certain algebraic data, e.g., by CR-algebras. We give an explicit formula which relates the Levi form of such an M and its higher order analogues to the Lie…
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.…
We classify the Lie algebras of infinitesimal CR automorphisms of weakly pseudoconvex hypersurfaces of finite multitype in $\mathbb C^N$. In particular, we prove that such manifolds admit neither nonlinear rigid automorphisms, nor real or…
In this paper, we study the real hypersurfaces $M$ in $\mathbb C^2$ at points $p\in M$ of infinite type. The degeneracy of $M$ at $p$ is assumed to be the least possible, namely such that the Levi form vanishes to first order in the CR…