Abstract: Since the scalar curvature appears in the term of Einstein field equations, the study of it becomes also important in general relativity. One of the open question about it is how to define the non-negative scalar curvature on non-smooth spaces. We will propose two definitions: one is the MV-scalar curvature on a closed topological manifold and the other one is n-volumic scalar curvatu...
AbstractThe scalar curvature of a Riemannian metric is interesting not only in analysis, geometry, and topology, but also in physics. Enlargeable Length-structures will be introduced and showed that it is a new obstruction to the existence of a Riemannian metric with positive scalar curvature (PSC-metric). Thus, the connected sum of a closed manifold with some of locally CAT(0)-manifolds carry ...