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pro vyhledávání: '"Rothschild, Linda Preiss"'
Autor:
Rothschild, Linda Preiss
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
Comment: 15 pages; dedicated to Robert Gre
Comment: 15 pages; dedicated to Robert Gre
Externí odkaz:
http://arxiv.org/abs/math/0304015
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 determination resul
Externí odkaz:
http://arxiv.org/abs/math/0012243
Iterated Segre mappings of real analytic generic submanifolds in complex space have been an essential tool in the study of holomorphic, formal, and CR mappings between such manifolds. In this paper we present a theory of iterated Segre mappings for s
Externí odkaz:
http://arxiv.org/abs/math/0008112
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 submanifolds M and
Externí odkaz:
http://arxiv.org/abs/math/0002186
We consider CR submersive mappings between generic submanifolds in complex space. We show that, under suitable conditions on the manifolds, there is an integer k such that any jet of the CR mapping at a given point is a rational function of its k-jet
Externí odkaz:
http://arxiv.org/abs/math/9811104
Let $M$ be a real analytic hypersurface in $\bC^N$ which is finitely nondegenerate, a notion that can be viewed as a generalization of Levi nondegenerate, at $p_0\in M$. We show that if $M'$ is another such hypersurface and $p'_0\in M'$, then the set
Externí odkaz:
http://arxiv.org/abs/math/9701201
In this paper we prove a general result of the ``Hopf lemma'' type for CR mappings, with nonidentically vanishing Jacobians, between real hypersurfaces in C^n with smooth or real analytic boundaries. Applications of this result to finiteness and holo
Externí odkaz:
http://arxiv.org/abs/math/9603203
Publikováno v:
Journal of the American Mathematical Society, 2000 Oct 01. 13(4), 697-723.
Externí odkaz:
https://www.jstor.org/stable/2646128
We give conditions under which a germ of a holomorphic mapping in $\Bbb C^N$, mapping an irreducible real algebraic set into another of the same dimension, is actually algebraic. Let $A\subset \bC^N$ be an irreducible real algebraic set. Assume that
Externí odkaz:
http://arxiv.org/abs/math/9510201
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 hypersurface
Externí odkaz:
http://arxiv.org/abs/math/9505202