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A characterization of maps in $H^{1} (B^{3}, S^{2})$ which can be approximated by smooth maps

F. Bethuel (1990)

Annales de l'I.H.P. Analyse non linéaire

A correction to a paper of H. King.

L. Reid (1987)

Inventiones mathematicae

A fixed point theorem for a class of multi-valued continuously differentiable maps

Gilles Fournier, Donald Violette (1987)

Annales Polonici Mathematici

A generalized sharp Whitney theorem for jets.

Charles Fefferman (2005)

Revista Matemática Iberoamericana

Suppose that, for each point x in a given subset E ⊂ Rn, we are given an m-jet f(x) and a convex, symmetric set σ(x) of m-jets at x. We ask whether there exist a function F ∈ Cm,w(Rn) and a finite constant M, such that the m-jet of F at x belongs to f(x) + Mσ(x) for all x ∈ E. We give a necessary and sufficient condition for the existence of such F, M, provided each σ(x) satisfies a condition that we call "Whitnet w-convexity".

A generic condition implying o-minimality for restricted C $^{\infty}$ -functions

Olivier Le Gal (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove that the expansion of the real field by a restricted C $^{\infty}$ -function is generically o-minimal. Such a result was announced by A. Grigoriev, and proved in a different way. Here, we deduce quasi-analyticity from a transcendence condition on Taylor expansions. This then implies o-minimality. The transcendance condition is shown to be generic. As a corollary, we recover in a simple way that there exist o-minimal structures that doesn’t admit analytic cell decomposition, and that there exist incompatible...

A metric tangential calculus.

Burroni, Elisabeth, Penon, Jacques (2010)

Theory and Applications of Categories [electronic only]

A Note on Right-Equivalence of Map-Germs.

Olaf von Grudzinski (1979)

Mathematische Zeitschrift

A Note on the Order of Determination of a Finitely Determined Germ.

Terence Gaffney (1979)

Inventiones mathematicae

A regularity lemma for functions of several variables.

Jean L. Journé (1988)

Revista Matemática Iberoamericana

We shall prove the following Theorem. Let Fs and Fu be two continuous transverse foliations with uniformly smooth leaves, of some manifold. If f is uniformly smooth along the leaves of Fs and Fu, then f is smooth.