A Poincaré inequality for Lipschitz intrinsic vector fields in the Heisenberg group
speaker: Giovanna Citti (Università di Bologna)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. This inequality has been already established in case of coefficients Lipchitz continuous in the standard Euclidean sense, but the intrinsic Lipschitz condition is weaker. Hence we will use a different technique based on approximation of the given vector fields with polynomial ones. These approximating vector fields satisfy a representation formula, from which we get the Poincaré inequality for the nonlinear vector fields.
timetable:
Thu 13 Oct, 14:30 - 15:20, Aula Dini
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