The two faces of scalar curvature

For zoom details contact Stephan Stadler (stadler@mpim...)

By Gromov’s h-principle there are no global obstructions against Riemannian metrics with prescribed curvature bounds on non-compact connected manifolds. Under additional assumptions, such as metric completeness or specific boundary conditions, this flexibility is challenged by rigidity phenomena which lead to classification patterns in terms of algebraic topological and metric invariants.

The geometry of Riemannian manifolds of positive scalar curvature lies at the border between the flexible and rigid worlds. I will illustrate this dual nature by some exemplary ideas and results.