A Frobenius-type theorem for singular Lipschitz distributions

@article{Montanari2011AFT,
  title={A Frobenius-type theorem for singular Lipschitz distributions},
  author={Annamaria Montanari and Daniele Morbidelli},
  journal={Journal of Mathematical Analysis and Applications},
  year={2011},
  volume={399},
  pages={692-700}
}
View PDF on arXiv
11 Citations
Background Citations
3

11 Citations

A Frobenius Theorem for Continuous Distributions in Dimension Three

We formulate a notion of "(uniform) asymptotic involutivity" and show that it implies (unique) integrability of two-dimensional continuous distributions in dimension three. This can be seen as a…

A Frobenius Theorem for Corank-1 Continuous Distributions in Dimensions two and three

We formulate a notion of (uniform) asymptotic involutivity and show that it implies (unique) integrability of corank-1 continuous distributions in dimensions three or less. This generalizes and…

Integrability of continuous bundles

We give new sufficient conditions for the integrability and unique integrability of continuous tangent subbundles on manifolds of arbitrary dimension, generalizing Frobenius’ classical theorem for…

Step-s involutive families of vector fields, their orbits and the Poincar\'e inequality

Almost Exponential Maps and Integrability Results for a Class of Horizontally Regular Vector Fields

We consider a family ${\mathcal{H}}:= \{X_1, \dots, X_m\}$ of C1 vector fields in ℝn and we discuss the associated ${\mathcal{H}}$-orbits. Namely, we assume that our vector fields belong to a…

Coordinates Adapted to Vector Fields: Canonical Coordinates

Given a finite collection of C1 vector fields on aC2 manifold which span the tangent space at every point, we consider the question of when there is locally a coordinate system in which these vector…

Beyond Hörmander’s Operators

In this last chapter I want to discuss some developments which have taken place in the study of Hormander’s operators and related topics since the 1990’s. As we will see, most of these developments…

Integral representations for bracket-generating multi-flows

If $f_1,f_2$ are smooth vector fields on an open subset of an Euclidean space and $[f_1,f_2]$ is their Lie bracket, the asymptotic formula \begin{equation}\label{abstract:EQ} …

Almost Exponential Maps and Integrability Results for a Class of Horizontally Regular Vector Fields

We consider a family \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…

On exterior differential systems involving differentials of Hölder functions

References

SHOWING 1-10 OF 26 REFERENCES

Frobenius-type theorems for Lipschitz distributions☆

Lipschitz distributions and Anosov flows

. We show that if a distribution is locally spanned by Lipschitz vector (cid:12)elds and is involutive a.e., then it is uniquely integrable giving rise to a Lipschitz foliation with leaves of class C…

The Complex Frobenius Theorem for Rough Involutive Structures

We establish a version of the complex Frobenius theorem in the context of a complex subbundle S of the complexified tangent bundle of a manifold, having minimal regularity. If the subbundle S defines…

Step-s involutive families of vector fields, their orbits and the Poincar\'e inequality

Commutators of flow maps of nonsmooth vector fields

Multi-parameter Carnot-Carathéodory balls and the theorem of Frobenius

We study multi-parameter Carnot-Caratheodory balls, generalizing results due to Nagel, Stein, and Wainger in the single parameter setting. The main technical result is seen as a uniform version of…

Almost Exponential Maps and Integrability Results for a Class of Horizontally Regular Vector Fields

We consider a family ${\mathcal{H}}:= \{X_1, \dots, X_m\}$ of C1 vector fields in ℝn and we discuss the associated ${\mathcal{H}}$-orbits. Namely, we assume that our vector fields belong to a…

Smooth Distributions Are Globally Finitely Spanned

Summary. A smooth distribution on a smooth manifold M is, by definition, a map that assigns to each point x of M a linear subspace Δ(x) of the tangent space T x M, in such a way that, locally, there…

Smooth distributions are globally finitely spanned

A smooth distribution on a smooth manifold M is, by definition, a map that assigns to each point x of M a linear subspace ∆(x) of the tangent space TxM , in such a way that, locally, there exist…

Orbits of families of vector fields and integrability of distributions

Let D be an arbitrary set of Cc vector fields on the Cc manifold M. It is shown that the orbits of D are C' submanifolds of M, and that, moreover, they are the maximal integral submanifolds of a…