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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...

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.

Minimizing the Energy of Maps from a surface into a 2-shpere with prescribed degree and boundary values.

Ernst Kuwert (1994)

Manuscripta mathematica

Morphisms of projective varieties from the viewpoint of minimal model theory [Book]

Marco Andreatta, Massimiliano Mella (2003)

Multiplicity and the Łojasiewicz exponent

S. Spodzieja (2000)

Annales Polonici Mathematici

We give a formula for the multiplicity of a holomorphic mapping $f : ℂ^{n} \supset Ω \to ℂ^{m}$ , 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.