In this paper we study the notion of regular surface in non homogeneous Lie groups. In particular we prove an implicitly function theorem and prove the regularity of the function implicitly defined. Indeed the implicit function theorem had already been proved in homogeneous Lie groups by [FSS], while the regularity problem of the function implicitly defined was still open even in the simplest Lie group.
Implicit function theorem in Carnot-Caratheodory spaces / Citti, G.; Manfredini, M.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 8:(2006), pp. 657-680. [10.1142/S0219199706002234]
Implicit function theorem in Carnot-Caratheodory spaces
M. Manfredini
2006
Abstract
In this paper we study the notion of regular surface in non homogeneous Lie groups. In particular we prove an implicitly function theorem and prove the regularity of the function implicitly defined. Indeed the implicit function theorem had already been proved in homogeneous Lie groups by [FSS], while the regularity problem of the function implicitly defined was still open even in the simplest Lie group.
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