Pinched manifolds becoming dull
Timothy Carson · Texas ScholarWorks (Texas Digital Library) · 2018
In this thesis, we prove short-time existence for Ricci flow, for a class of metrics with unbounded curvature. Our primary motivation in investigating this class of metrics is that it includes many final-time limits of Ricci flow singularities. Well known examples include neckpinches and degenerate neckpinches. We provide an example of Ricci flow modifying a neighborhood of a manifold with the topological change [mathematical equation], although we only rigorously deal with the second part of the transformation. We also provide forward evolution from some manifolds with ends of infinite length and unbounded curvature, such as the submanifold given by [mathematical equation]. In this example, the two ends with unbounded curvature immediately become compact and with bounded curvature, so the topology of the forward evolution is S³.