Universität Augsburg
Institut für Mathematik

On connected manifolds of dimension at least two and with nonempty boundary the existence of Riemannian metrics with positive scalar curvature is unobstructed, unlike on closed manifolds.

We discuss a number of geometric boundary conditions, such as being of non-negative mean curvature, totally geodesic, doubling or of product form near the boundary, which lead to nontrivial existence and classification results for positive scalar curvature metrics.

To this end, we formulate a general deformation principle that implies that the relaxation of boundary conditions often leads to weak homotopy equivalences of spaces of positive scalar curvature metrics. However, this is not true for the condition of being of product form near the boundary, which is often used by topologists.

Joint work with Christian Bär (Potsdam).