# Functions convex along vector fields

## Venerdi' 19 Novembre 2010 - Federica Dragoni

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Venerdi' 19 novembre 2010 alle ore 12:15 in aula 1BC45 Federica Dragoni (Universita' di Padova) terra' un seminario dal titolo "Functions convex along vector fields".

-Abstract
We introduce a new notion of convexity which generalizes the standard convexity to non-Euclidean structures. This notion applies in particular to sub-Riemannian geometries and it is equivalent to the known horizontal convexity in any Carnot group. We then show some properties of functions which are convex in the sense of our definition (namely $X$-convex functions) and their characterization through the sign of the intrinsic Hessian.

Rif. int. M. Bardi, P. Mannucci, C. Marchi