Alessia Kogoj Università di Urbino
Liouville theorems in sub-Riemannian settings
We present some Liouville-type theorems, related to evolution operators and to
their "time"-stationary counterpart. The operators we are dealing with are left
translations invariant on a Lie group structure and, in some cases, are
homogeneous with respect to a group of dilations. In all these cases the
operators have smooth coefficients and are hypoelliptic at least in a
neighborhood of the origin. We also present a polynomial Liouville-type theorem
for X-elliptic operators with nonsmooth coefficients, by extending to this new
setting a celebrated result by Colding and Minicozzi related to the
Laplace-Beltrami operator on Riemannian manifolds.
The results are contained in a series of papers in collaboration with A.
Bonfiglioli, E. Lanconelli, Y.Pinchover, S. Polidoro and E. Priola.