IMPLICIT FUNCTION THEOREM IN CARNOT–CARATHÉODORY SPACES

By Giovanna Citti, Maria Manfredini. 2006

52 citations recorded by the source corpus.

In this paper, we prove an implicit function theorem and we study the regularity of the function implicitly defined. The implicit function theorem had already been proved in homogeneous Lie groups by Franchi, Serapioni and Serra Cassano, while the regularity problem of the function implicitly defined was still open even in the simplest Lie group.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6725131cdd4e930ddf6d37ff4dddb8b5715016b2

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In Applied Mathematics

In Astronomy and Astrophysics

In Mathematical Physics

Citations in the corpus

Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups , n > 1 (2010, background): “According to a version of the implicit function theorem ([22] and [13]), any level surface {f (s, x) = c} ⊂ H n of functions f : H n → R with continuous derivatives along the directions (1.1), can locally (near non-characteristic points) be expressed as an intrinsic graph of a function u : Ω → R, Ω…”
Characterizations of intrinsic rectifiability in Heisenberg groups (2010, background): “A systematic study of H-regular surfaces has been recently carried out in [4, 5, 11, 17].”
Differentiability of Intrinsic Lipschitz Functions within Heisenberg Groups (2011, background): “Indeed, implicit function theorems for groups [10, 11, 17, 18, 21] state precisely that these level sets are always, locally, intrinsic graphs.”
Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs (2009, unknown): “1”