On CR singular CR images

2021 ◽  
pp. 2150090
Author(s):  
Jiří Lebl ◽  
Alan Noell ◽  
Sivaguru Ravisankar
Keyword(s):  
Holomorphic Functions ◽  
Independent Interest ◽  
Holomorphic Map ◽  
Cr Structure ◽  
Quadratic Invariants ◽  
Real Analytic ◽  
The Stability ◽  
Cr Submanifolds

We say that a CR singular submanifold [Formula: see text] has a removable CR singularity if the CR structure at the CR points of [Formula: see text] extends through the singularity as an abstract CR structure on [Formula: see text]. We study such real-analytic submanifolds, in which case removability is equivalent to [Formula: see text] being the image of a generic real-analytic submanifold [Formula: see text] under a holomorphic map that is a diffeomorphism of [Formula: see text] onto [Formula: see text], what we call a CR image. We study the stability of the CR singularity under perturbation, the associated quadratic invariants, and conditions for removability of a CR singularity. A lemma is also proved about perturbing away the zeros of holomorphic functions on CR submanifolds, which could be of independent interest.

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

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.

scholarly journals Damping estimates for oscillatory integral operators with real-analytic phases and its applications

2019 ◽  
Vol 31 (4) ◽  
pp. 843-865
Author(s):  
Zuoshunhua Shi ◽  
Shaozhen Xu ◽  
Dunyan Yan
Keyword(s):  
Integral Operators ◽  
Oscillatory Integral ◽  
Independent Interest ◽  
One Dimensional ◽  
Oscillatory Integral Operators ◽  
Real Analytic

Abstract In this paper, we investigate sharp damping estimates for a class of one-dimensional oscillatory integral operators with real-analytic phases. By establishing endpoint estimates for suitably damped oscillatory integral operators, we are able to give a new proof of the sharp {L^{p}} estimates, which have been proved by Xiao in [Endpoint estimates for one-dimensional oscillatory integral operators, Adv. Math. 316 2017, 255–291]. The damping estimates obtained in this paper are of independent interest.

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

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.

scholarly journals Harmonic Maps and Stability onf-Kenmotsu Manifolds

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Vittorio Mangione
Keyword(s):  
Harmonic Maps ◽  
Riemannian Submersions ◽  
Kenmotsu Manifold ◽  
Holomorphic Map ◽  
Kenmotsu Manifolds ◽  
The Stability ◽  
Kählerian Manifold

The purpose of this paper is to study some submanifolds and Riemannian submersions on anf-Kenmotsu manifold. The stability of aϕ-holomorphic map from a compactf-Kenmotsu manifold to a Kählerian manifold is proven.

scholarly journals Heavy handed quest for fixed points in multiple coupling scalar theories in the ε expansion

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hugh Osborn ◽  
Andreas Stergiou
Keyword(s):  
Fixed Points ◽  
Index Case ◽  
Symmetric Tensors ◽  
Number Of Solutions ◽  
Stability Matrix ◽  
Negative Eigenvalues ◽  
Large Numbers ◽  
Quadratic Invariants ◽  
Scalar Theories ◽  
The Stability

Abstract The tensorial equations for non trivial fully interacting fixed points at lowest order in the ε expansion in 4 − ε and 3 − ε dimensions are analysed for N-component fields and corresponding multi-index couplings λ which are symmetric tensors with four or six indices. Both analytic and numerical methods are used. For N = 5, 6, 7 in the four-index case large numbers of irrational fixed points are found numerically where ‖λ‖2 is close to the bound found by Rychkov and Stergiou [1]. No solutions, other than those already known, are found which saturate the bound. These examples in general do not have unique quadratic invariants in the fields. For N ⩾ 6 the stability matrix in the full space of couplings always has negative eigenvalues. In the six index case the numerical search generates a very large number of solutions for N = 5.

A class of four-dimensional CR submanifolds in six dimensional nearly Kähler manifolds

2018 ◽  
Vol 68 (5) ◽  
pp. 1129-1140
Author(s):  
Miroslava Antić
Keyword(s):  
Three Dimensional ◽  
Kähler Manifolds ◽  
Moving Frame ◽  
Kahler Manifolds ◽  
Twisted Product ◽  
Totally Geodesic ◽  
Cr Structure ◽  
Nearly Kähler ◽  
Nearly Kähler Manifolds ◽  
Cr Submanifolds

Abstract We investigate four-dimensional CR submanifolds in six-dimensional strict nearly Kähler manifolds. We construct a moving frame that nicely corresponds to their CR structure and use it to investigate CR submanifolds that admit a special type of doubly twisted product structure. Moreover, we single out a class of CR submanifolds containing this type of doubly twisted submanifolds. Further, in a particular case of the sphere $ \mathbb{S}^{6}(1) $, we show that the two families of four-dimensional CR submanifolds, those that admit a three-dimensional geodesic distribution and those ruled by totally geodesic spheres $ \mathbb{S}^{3} $ coincide, and give their classification, which as a subfamily contains a family of doubly twisted CR submanifolds.

scholarly journals On the stability of pseudoconvexity for certain covering spaces

1997 ◽  
Vol 147 ◽  
pp. 107-112 ◽  
Author(s):  
Takeo Ohsawa
Keyword(s):  
Covering Spaces ◽  
Holomorphic Map ◽  
One Dimensional ◽  
Covering Map ◽  
Proper Holomorphic Map ◽  
The Stability

AbstractIt is proved that, if is a proper holomorphic map with one-dimensional fibers and a covering map, a point t ∈ T has a neighbourhood U such that is holomorphically convex if and only if is holomorphically convex.

scholarly journals Composition operators on Qp spaces

2001 ◽  
Vol 70 (2) ◽  
pp. 161-188 ◽  
Author(s):  
Zengjian Lou
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Function Space ◽  
Composition Operators ◽  
Bloch Space ◽  
Dirichlet Space ◽  
Holomorphic Functions ◽  
Bloch Spaces ◽  
Holomorphic Map ◽  
Analytic Function Space

AbstractA holomorphic map ψ of the unit disk ito itself induces an operator Cψ on holomorphic functions by composition. We characterize bounded and compact composition operators Cψ on Qp spaces, which coincide with the BMOA for p = 1 and Bloch spaces for p > 1. We also give boundedness and compactness characterizations of Cψ from analytic function space X to Qp spaces, X = Dirichlet space D, Bloch space B or B0 = {f: f′ ∈ H∞}.

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