相关论文: Construction of counterexamples to the $2-$jet det…

One constructs an example of a generic quadratic submanifold of codimension $5$ in $\Bbb C^9$ which admits a real analytic infinitesimal CR automorphism with homogeneous polynomial coefficients of degree $3.$

Counterexamples to the 2-jet determination Chern-Moser Theorem in codimension d>2 have recently been constructed. We extend the Chern-Moser approach for hypersurfaces to real submanifolds of higher codimension in complex space to derive…

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…

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…

We classify polynomial models for real hypersurfaces in $\mathbb C^N$, which admit nonlinearizable infinitesimal CR automorphisms. As a consequence, this provides an optimal 1-jet determination result in the general case. Further we prove…

Local CR-generic submanifolds of C^N are in one-to-one correspondence with their respective graphing functions, but it is well known that (despite their importance) the Cartan-Hachtroudi-Chern-Moser invariants and coframes for Levi…

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…

Let $M^3 \subset \mathbb{C}^2$ be a $\mathcal{C}^\omega$ Levi nondegenerate hypersurface. In the literature, Cartan-Moser chains are detected from rather advanced considerations: either from the construction of a Cartan connection…

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 first construct closed spherical CR manifolds of dimension at least five having non-trivial first Chern class with real coefficients. We next prove a constraint on Chern classes with real coefficients of (not necessarily closed)…

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…

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 condition amounts to a holomorphic extension property for the…

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'…

We prove the following finite jet determination result for CR mappings: Given a smooth generic submanifold M of C^N, N >= 2, which is essentially finite and of finite type at each of its points, for every point p on M there exists an…

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…

We give a complete classification of polynomial models for smooth real hypersurfaces of finite Catlin multitype in $\mathbb C^3$, which admit nonlinear infinitesimal CR automorphisms. As a consequence, we obtain a sharp 1-jet determination…

It is well known that the Eisenbud-Goto regularity conjecture is true for arithmetically Cohen-Macaulay varieties, projective curves, smooth surfaces, smooth threefolds in $\mathbb{P}^5$, and toric varieties of codimension two. After J.…

We establish 2-jet determinacy for the symmetry algebra of the underlying structure of any (complex or real) parabolic geometry. At non-flat points, we prove that the symmetry algebra is in fact 1-jet determined. Moreover, we prove 1-jet…

We prove the following Artin type approximation theorem for smooth CR mappings: given M a connected real-analytic CR submanifold in C^N that is minimal at some point, M' a real-analytic subset of C^N', and H:M->M' a smooth CR mapping, there…

We generalise the classical Chern-Gauss-Bonnet formula to a class of 4-dimensional manifolds with finitely many conformally flat ends and singular points. This extends results of Chang-Qing-Yang in the smooth case. Under the assumptions of…