Modul:   MAT673  Seminar PDE and Mathematical Physics

Some new results on sub-Riemannian geodesics in stratified groups

Talk by Dr. Davide Vittone

Date: 17.03.14  Time: 17.15 - 19.00  Room: Y27H25

We present some result on sub-Riemannian geodesics in stratified groups recently obtained in collaboration with E. Le Donne, G. P. Leonardi, and R. Monti. A sub-Riemannian manifold is a manifold M endowed with a distinguished subbundle HM of the tangent bundle TM and with a metric on HM. A distance (called sub-Riemannian) on M can be defined on minimizing the length among curves which are tangent to HM. One of the main open problems in the field is the regularity of length minimizers, that is not trivial due to the presence of the so called abnormal curves. We provide a characterization of abnormal curves in stratified groups showing that they are contained in certain algebraic varieties; applications to the problem of geodesics' regularity will be discussed.