# A Poincaré inequality for Lipschitz intrinsic vector fields in the Heisenberg group

## Giovanna Citti

### (Dipartimento di Matematica, Universita' di Bologna)

Date: Oct 13, 2011, time: 14:30

Place: Centro De Giorgi, Scuola Normale Superiore

Abstract. This result is a joint work with M.Manfredini, A.Pinamonti, F.Serra Cassano. We prove a Poincaré inequality for Lipschitz
intrinsic vector fields in any Heisenberg group of dimension $n>1$.
If a subriemannian metric is defined in this group, a regular surface
implicitly defines a graph $\phi$, which is regular with respect
to non linear vector fields, defined in terms of $\phi$ itself.
Geometric equations can be written in terms of these nonlinear vector fields.
Hence it is necessary to establish a Poincaré formula for vector
fields with minimal assumptions on the coefficients.