From a constructive point of view one observes that there is a natural upper bound but no lower bound for the curvature on a given manifold with fixed coarse data on its metric geometry: while decreasing curvatures one observes flexibility phenomena. Motivated by observations of this kind we are tempted to think of an individual curvature content of a given manifold depending of course on the curvature problem under consideration. Within this project we will focus on scalar curvature. On the one hand we will look for new and refined existence results for curvature decreasing operations and secondly for some new techniques in order to detect obstructions and constraints for the existence of certain positive scalar curvature configurations.
DFG Programme
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