Speaker
David Krejcirik
Description
We introduce a notion of magnetic field in the
Heisenberg group and we study its influence on spectral properties
of the corresponding magnetic (sub-elliptic) Laplacian. We show that uniform magnetic fields uplift the bottom of the spectrum. For magnetic fields vanishing at infinity,
including Aharonov-Bohm potentials, we derive magnetic improvements to a variety of Hardy-type inequalities for the Heisenberg sub-Laplacian. In particular, we establish a sub-Riemannian analogue of Laptev and Weidl sub-criticality result for magnetic Laplacians in the plane. This is joint work with Biagio Cassano, Valentina Franceschi and Dario Prandi.
