Orateur
Armin Schikorra
(U. Pittsburgh, États-Unis)
Description
The Heisenberg groups are examples of sub-Riemannian manifolds homeomorphic, but not diffeomorphic to the Euclidean space. Their metric is derived from curves which are only allowed to move in so-called horizontal directions.
When one considers approximation or extension problems for Sobolev maps into the Riemannian manifolds it is known that topological properties of the target manifold play a role. However, due to the homeomorphism, the topology of the Heisenberg group is the same as the Euclidean space. A notion of Hölder topology is needed. I will report on some progress (with Hajlasz) on some topological features of the Heisenberg group, in particular on an embedding question due to Gromov.
Author
Armin Schikorra
(U. Pittsburgh, États-Unis)
Co-auteur
Piotr Hajlasz
(U. Pittsburgh, États-Unis)
