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

## Tags » Compactness And Contradiction

#### 285G, Lecture 12: High curvature regions of Ricci flow and κ-solutions

In previous lectures, we have established (modulo some technical details) two significant components of the proof of the Poincaré conjecture: finite time extinction of Ricci flow with surgery (Theorem 4 of… 3,351 more words