Proceedings of the American Mathematical Society
We introduce a notion of wave maps with a target in the sub- Riemannian Heisenberg group and study their relation with Riemannian wave maps with range in Lagrangian submanifolds. As an application we establish existence and eventually ill-posedness of the corresponding Cauchy problem.
Heisenberg group, Wave maps
Capogna, Luca and Shatah, Jalal, "A Note on Ill-Posedness of the Cauchy Problem for Heisenberg Wave Maps" (2008). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.