On the problem of the linearization of the stability group of a real-analytic hypersurface

A connected real analytic hypersurface M⊂Cn+1 whose Levi form is nondegenerate in at least one point—hence at every point of some Zariski-dense open subset—is locally biholomorphic to the model Heisenberg quadric pseudosphere of signature (k,n-k) in one point if and only if, at every other Levi nondegenerate point, it is also locally biholomorphic to some Heisenberg pseudosphere, possibly having a different signature (l,n-l). Up to signature, pseudosphericity then jumps across the Levi degenerate locus and in particular across the nonminimal locus, if there exists any.

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On the Construction of Large Algebras Not Contained in the Image of the Borel Map

Results in Mathematics ◽

10.1007/s00025-019-1146-0 ◽

2019 ◽

Vol 75 (1) ◽

Author(s):

Céline Esser ◽

Gerhard Schindl

Keyword(s):

Sequence Space ◽

Analytic Functions ◽

General Setting ◽

Smooth Functions ◽

The Real ◽

Cauchy Product ◽

Real Analytic Functions ◽

Borel Map ◽

Real Analytic ◽

The Stability

AbstractThe Borel map $$j^{\infty }$$j∞ takes germs at 0 of smooth functions to the sequence of iterated partial derivatives at 0. It is well known that the restriction of $$j^{\infty }$$j∞ to the germs of quasianalytic ultradifferentiable classes which are strictly containing the real analytic functions can never be onto the corresponding sequence space. In a recent paper the authors have studied the size of the image of $$j^{\infty }$$j∞ by using different approaches and worked in the general setting of quasianalytic ultradifferentiable classes defined by weight matrices. The aim of this paper is to show that the image of $$j^{\infty }$$j∞ is also small with respect to the notion of algebrability and we treat both the Cauchy product (convolution) and the pointwise product. In particular, a deep study of the stability of the considered spaces under the pointwise product is developed.

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On the Class of the Stability Group of a Series of Subgroups

Journal of the London Mathematical Society ◽

10.1112/jlms/s2-41.1.33 ◽

1990 ◽

Vol s2-41 (1) ◽

pp. 33-41

Author(s):

T. C. Hurley

Keyword(s):

Stability Group ◽

The Stability

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On the stability group of CR manifolds

Comptes Rendus Mathematique ◽

10.1016/j.crma.2006.06.016 ◽

2006 ◽

Vol 343 (3) ◽

pp. 169-172

Author(s):

Bernhard Lamel ◽

Nordine Mir

Keyword(s):

Cr Manifolds ◽

Stability Group ◽

The Stability

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Analytic Jet Parametrization for CR Automorphisms of Some Essentially Finite CR Manifolds

Nagoya Mathematical Journal ◽

10.1017/s0027763000009533 ◽

2008 ◽

Vol 189 ◽

pp. 155-168

Author(s):

Sung-Yeon Kim

Keyword(s):

Uniform Convergence ◽

Lie Group ◽

Group Structure ◽

Cr Manifolds ◽

Real Analytic ◽

The Stability

AbstractIn this paper we construct analytic jet parametrizations for the germs of real analytic CR automorphisms of some essentially finite CR manifolds on their finite jet at a point. As an application we show that the stability groups of such CR manifolds have Lie group structure under composition with the topology induced by uniform convergence on compacta.

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