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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 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 : n Ω 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.

Non-deformability of entire curves in projective hypersurfaces of high degree

Olivier Debarre, Gianluca Pacienza, Mihai Păun (2006)

Annales de l’institut Fourier

In this article, we prove that there does not exist a family of maximal rank of entire curves in the universal family of hypersurfaces of degree d 2 n in the complex projective space n . This can be seen as a weak version of the Kobayashi conjecture asserting that a general projective hypersurface of high degree is hyperbolic in the sense of Kobayashi.

Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy

Javier Ribón (2009)

Annales de l’institut Fourier

The formal class of a germ of diffeomorphism ϕ is embeddable in a flow if ϕ is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at n ( n > 1 ) whose formal class is non-embeddable. The examples are inside a family in which the non-embeddability is of geometrical type. The proof relies on the properties of some linear functional operators that we obtain through the study of polynomial families of diffeomorphisms...

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