# 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} }

## 11 Citations

### A Frobenius Theorem for Continuous Distributions in Dimension Three

- Mathematics
- 2014

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

- Mathematics
- 2014

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

- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2019

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

- Mathematics
- 2011

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

- Mathematics
- 2013

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

- MathematicsGeometric and Functional Analysis
- 2018

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

- Mathematics
- 2014

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

- Mathematics
- 2015

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

- Materials SciencePotential Analysis
- 2012

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

- MathematicsJournal of Differential Equations
- 2022

## References

SHOWING 1-10 OF 26 REFERENCES

### Lipschitz distributions and Anosov flows

- Mathematics
- 1996

. 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

- Mathematics
- 2006

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

- Mathematics
- 2011

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

- Mathematics
- 2009

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

- Mathematics
- 2013

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

- Mathematics
- 2008

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

- Mathematics
- 2007

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

- Mathematics
- 1973

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…