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- Andrei A. Agrachev, Ugo V. Boscain, Gregoire Charlot, Roberta Ghezzi, Mario Sigalotti
- Proceedings of the 48h IEEE Conference onâ€¦
- 2009

Two dimensional almost-Riemannian geometries are metric structures on surfaces defined locally by a Lie bracket generating pair of vector fields. We study the relation between the topology of anâ€¦ (More)

We give a notion of BV function on an oriented manifold where a volume form and a family of lower semicontinuous quadratic forms Gp : TpM â†’ [0,âˆž] are given. When we consider sub-Riemannian manifolds,â€¦ (More)

Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that canâ€¦ (More)

- Bernard Bonnard, Gregoire Charlot, Roberta Ghezzi, Gabriel Janin
- 2017

We study the tangential case in 2-dimensional almost-Riemannian geometry. We analyse the connection with the Martinet case in sub-Riemannian geometry. We compute estimations of the exponential mapâ€¦ (More)

Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that canâ€¦ (More)

The main motivation of this paper arises from the study of Carnotâ€“CarathÃ©odory spaces, where the class of 1-rectifiable sets does not contain smooth non-horizontal curves; therefore a new definitionâ€¦ (More)

This paper is a starting point towards computing the Hausdorff dimension of submanifolds and the Hausdorff volume of small balls in a sub-Riemannian manifold with singular points. We first considerâ€¦ (More)

In this paper we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it with a smooth volume. We first give the Lebesgue decomposition of the Hausdorff volume. Thenâ€¦ (More)

- Marco Caponigro, Roberta Ghezzi, Benedetto Piccoli, Emmanuel Trélat
- IEEE Transactions on Automatic Control
- 2018

In the control theory, the term chattering is used to refer to fast oscillations of controls, such as an infinite number of switchings over a finite time interval. In this paper, we focus on threeâ€¦ (More)

Contents Chapter 1. Introduction 1 1. History 1 2. Motivations 3 3. Examples of metric measure spaces 4 Chapter 2. H-Sobolev space and first tools of differential calculus 9 1. Relaxed slope andâ€¦ (More)

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