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Manifolds with a unique embedding

Zbigniew Jelonek (2009)

Colloquium Mathematicae

We show that if X, Y are smooth, compact k-dimensional submanifolds of ℝⁿ and 2k+2 ≤ n, then each diffeomorphism ϕ: X → Y can be extended to a diffeomorphism Φ: ℝⁿ → ℝⁿ which is tame (to be defined in this paper). Moreover, if X, Y are real analytic manifolds and the mapping ϕ is analytic, then we can choose Φ to be also analytic. We extend this result to some interesting categories of closed (not necessarily compact) subsets of ℝⁿ, namely, to the category of Nash submanifolds...

Maximal and area integral characterizations of Hardy-Soboley spaces in the unit ball of Cn.

Patrick Ahern, Joaquim Bruna (1988)

Revista Matemática Iberoamericana

In this paper we deal with several characterizations of the Hardy-Sobolev spaces in the unit ball of Cn, that is, spaces of holomorphic functions in the ball whose derivatives up to a certain order belong to the classical Hardy spaces. Some of our characterizations are in terms of maximal functions, area functions or Littlewood-Paley functions involving only complex-tangential derivatives. A special case of our results is a characterization of Hp itself involving only complex-tangential derivatives....

Meromorphic extension spaces

Le Mau Hai, Nguyen Van Khue (1992)

Annales de l'institut Fourier

The aim of the present paper is to study meromorphic extension spaces. The obtained results allow us to get the invariance of meromorphic extendibility under finite proper surjective holomorphic maps.

Méthodes de changement d’échelles en analyse complexe

François Berteloot (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Nous mettons en perspective différentes méthodes de changement d’échelles et illustrons leur pertinence en mettant sur pieds des preuves simples et élémentaires de plusieurs théorèmes biens connus en analyse ou géométrie complexe. Les situations abordées sont variées et la plupart des théorèmes démontrés sont des classiques initialement obtenus entre la fin du xixe  et la seconde moitié du xxe  siècle.

Multiple values and uniqueness problem for meromorphic mappings sharing hyperplanes

Ting-Bin Cao, Kai Liu, Hong-Zhe Cao (2013)

Annales Polonici Mathematici

The purpose of this article is to deal with multiple values and the uniqueness problem for meromorphic mappings from ℂ m into the complex projective space ℙⁿ(ℂ) sharing hyperplanes. We obtain two uniqueness theorems which improve and extend some known results.

Multiplicity and the Łojasiewicz exponent

S. Spodzieja (2000)

Annales Polonici Mathematici

We give a formula for the multiplicity of a holomorphic mapping f : ℂ n ⊃ Ω → ℂ m , m > n, at an isolated zero, in terms of the degree of an analytic set at a point and the degree of a branched covering. We show that calculations of this multiplicity can be reduced to the case when m = n. We obtain an analogous result for the local Łojasiewicz exponent.

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