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On the analytic approximation of differentiable functions from above

Alessandro Tancredi, Alberto Tognoli (2002)

Bollettino dell'Unione Matematica Italiana

We determine conditions in order that a differentiable function be approximable from above by analytic functions, being left invariate on a fixed analytic subset which is a locally complete intersection.

On the group of real analytic diffeomorphisms

Takashi Tsuboi (2009)

Annales scientifiques de l'École Normale Supérieure

The group of real analytic diffeomorphisms of a real analytic manifold is a rich group. It is dense in the group of smooth diffeomorphisms. Herman showed that for the n -dimensional torus, its identity component is a simple group. For U ( 1 ) fibered manifolds, for manifolds admitting special semi-free U ( 1 ) actions and for 2- or 3-dimensional manifolds with nontrivial U ( 1 ) actions, we show that the identity component of the group of real analytic diffeomorphisms is a perfect group.

Real algebraic spaces

Andrew John Sommese (1977)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Real analytic manifolds in n with parabolic complex tangents along a submanifold of codimension one

Patrick Ahern, Xianghong Gong (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

We will classify n -dimensional real submanifolds in n which have a set of parabolic complex tangents of real dimension n - 1 . All such submanifolds are equivalent under formal biholomorphisms. We will show that the equivalence classes under convergent local biholomorphisms form a moduli space of infinite dimension. We will also show that there exists an n -dimensional submanifold M in n such that its images under biholomorphisms ( z 1 , , z n ) ( r z 1 , , r z n - 1 , r 2 z n ) , r > 1 , are not equivalent to M via any local volume-preserving holomorphic...

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