Universität Augsburg
Institut für Mathematik

Based on the existence of Riemannian metrics of positive scalar curvature on each connected manifold of dimension at least two and with nonempty boundary, we look at such metrics that fulfill certain additional boundary conditions.

The latter concern the second fundamental form or mean curvature. The question at hand is whether one can realize a desired behavior near the boundary by deforming given metrics.

In fact, there is a general deformation principle if it does not come along with mean curvature increase. This was proven by Bär and Hanke in case of manifolds with compact boundary. I will explain how to generalize the result to the noncompact case, investigating the topology of the boundary.