# $\mathcal{X}$-convexity and applications

## Federica Dragoni

### (University of Cardiff)

Date: Oct 11, 2011, time: 10:40

Place: Centro De Giorgi, Scuola Normale Superiore

Abstract. |
(joint work with Martino Bardi)|
We introduce a new notion of convexity, namely $\mathcal{X}$-convexity, which applies to any given family of vector fields and in particular to the sub-Riemannian case.|
We then show a PDE-characterization for $\mathcal{X}$-convex functions and we investigate some properties of these functions.