## 20 Citations

### Privileged Coordinates and Nilpotent Approximation for Carnot Manifolds, II. Carnot Coordinates

- MathematicsJournal of Dynamical and Control Systems
- 2019

This paper is a sequel of Choi and Ponge (J Dyn Control Syst 25:109–157, 2019) and deals with privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold, it is meant…

### Privileged Coordinates and Nilpotent Approximation for Carnot Manifolds, II. Carnot Coordinates

- MathematicsJournal of Dynamical and Control Systems
- 2019

This paper is a sequel of Choi and Ponge (J Dyn Control Syst 25:109–157, 2019) and deals with privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold, it is meant…

### Privileged Coordinates and Nilpotent Approximation of Carnot Manifolds, I. General Results

- MathematicsJournal of Dynamical and Control Systems
- 2018

In this paper, we attempt to give a systematic account on privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold, it is meant a manifold with a distinguished…

### A transverse index theorem in the calculus of filtered manifolds

- Mathematics
- 2022

We use ﬁltrations of the tangent bundle of a manifold starting with an integrable subbundle to deﬁne transverse symbols to the corresponding foliation, deﬁne a condition of transversally Rockland and…

### Privileged Coordinates and Nilpotent Approximation of Carnot Manifolds, I. General Results

- MathematicsJournal of Dynamical and Control Systems
- 2018

In this paper, we attempt to give a systematic account on privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold, it is meant a manifold with a distinguished…

### Euler-Like Vector Fields, Deformation Spaces and Manifolds with Filtered Structure

- MathematicsDocumenta Mathematica
- 2018

The first purpose of this note is to comment on a recent article of Bursztyn, Lima and Meinrenken, in which it is proved that if M is a smooth submanifold of a manifold V, then there is a bijection…

### Tangent groupoid and tangent cones in sub-Riemannian geometry

- Mathematics
- 2022

Let X 1 , ¨ ¨ ¨ , X m be vector ﬁelds satisfying Hörmander’s Lie bracket generating condition on a smooth manifold M . We generalise Connes’s tangent groupoid, by constructing a com-pletion of the…

### The Heat Asymptotics on Filtered Manifolds

- MathematicsJournal of geometric analysis
- 2020

A universal heat kernel expansion for formally self-adjoint non-negative Rockland differential operators on general closed filtered manifolds is established and Weyl’s law for the eigenvalue asymptotics is described.

### Pseudodifferential operators on filtered manifolds as generalized fixed points

- Mathematics
- 2021

On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension…

### A pseudodifferential calculus for maximally hypoelliptic operators and the Helffer-Nourrigat conjecture

- Mathematics
- 2022

We extend the classical regularity theorem of elliptic operators to maximally hypoelliptic differential operators. More precisely, given vector fields X1, . . . , Xm on a smooth manifold which…

## References

SHOWING 1-10 OF 83 REFERENCES

### Privileged Coordinates and Nilpotent Approximation for Carnot Manifolds, II. Carnot Coordinates

- MathematicsJournal of Dynamical and Control Systems
- 2019

This paper is a sequel of Choi and Ponge (J Dyn Control Syst 25:109–157, 2019) and deals with privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold, it is meant…

### Privileged Coordinates and Nilpotent Approximation of Carnot Manifolds, I. General Results

- MathematicsJournal of Dynamical and Control Systems
- 2018

In this paper, we attempt to give a systematic account on privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold, it is meant a manifold with a distinguished…

### On Carnot-Carathéodory metrics

- Mathematics
- 1985

Consider a smooth Riemannian ^-manifold (M, g) equipped with a smooth distribution of /c-planes. Such a distribution Δ assigns to each point m e M a /^-dimensional subspace of the tangent space TmM.…

### The tangent grupoid of a Heisenberg manifold

- Mathematics
- 2006

As a step towards proving an index theorem for hypoelliptic operators on Heisenberg manifolds, including for those on CR and contact manifolds, we construct an analogue for Heisenberg manifolds of…

### The Geometry of the Osculating Nilpotent Group Structures of the Heisenberg Calculus

- Mathematics
- 2010

We explore the geometry that underlies the osculating nilpotent group structures of the Heisenberg calculus. For a smooth manifold $M$ with a distribution $H\subseteq TM$ analysts use explicit (and…

### Sub-riemannian geometry from intrinsic viewpoint

- Mathematics
- 2012

Gromov proposed to extract the (di erential) geometric content of a sub-riemannian space exclusively from its Carnot-Carath eodory distance. One of the most striking features of a regular…

### The differential of a quasi-conformal mapping of a Carnot-Caratheodory space

- Mathematics
- 1995

The theory of quasi-conformal mappings has been used to prove rigidity theorems on hyperbolic n space over the division algebras ℝ, ℂ, ℍ, and \({\Bbb O}\), by studying quasi-conformal mappings on…

### The Atiyah-Singer index formula for subelliptic operators on contact manifolds. Part I

- Mathematics
- 2008

The Atiyah-Singer index theorem gives a topological formula for the index of an elliptic differential operator. The topological index depends on a cohomology class that is constructed from the…

### Euler-Like Vector Fields, Deformation Spaces and Manifolds with Filtered Structure

- MathematicsDocumenta Mathematica
- 2018

The first purpose of this note is to comment on a recent article of Bursztyn, Lima and Meinrenken, in which it is proved that if M is a smooth submanifold of a manifold V, then there is a bijection…