On Weak Super Ricci Flow through Neckpinch

Abstract In this article, we study the Ricci flow neckpinch in context of metric measure spaces. We introduce notion a spacetime and weak (refined) super associated to convex cost functions (cost which are increasing distance function). Our definition is based on coupled contraction property for suitably defined diffusions maximal diffusion subspaces. our main theorem, show that if non-degenerate spherical can be continued beyond singular time by smooth forward evolution then corresponding through singularity (and therefore all) only single point pinching phenomenon holds at times; i.e., singularities form finite number totally geodesic hypersurfaces { x } ×