Tags » Geometric Limits

285G, Lecture 18: The structure of high-curvature regions of Ricci flow

Having characterised the structure of -solutions, we now use them to describe the structure of high curvature regions of Ricci flow, as promised back in… 3,148 more words


285G, Lecture 17: The structure of κ-solutions

Having classified all asymptotic gradient shrinking solitons in three and fewer dimensions in the previous lecture, we now use this classification, combined with extensive use of compactness and contradiction arguments, as well as the comparison geometry of complete Riemannian manifolds of non-negative curvature, to understand the structure of -solutions in these dimensions, with the aim being to state and prove precise versions of Theorem 1 and Corollary 1 from… 3,669 more words


285G, Lecture 16: Classification of asymptotic gradient shrinking solitons

In the previous lecture, we showed that every -solution generated at least one asymptotic gradient shrinking soliton . This soliton is known to have the following properties: 3,426 more words


285G, Lecture 15: Geometric limits of Ricci flows, and asymptotic gradient shrinking solitons

We now begin using the theory established in the last two lectures to rigorously extract an asymptotic gradient shrinking soliton from the scaling limit of any given -solution. 3,832 more words