4 papers
The PDE-ODI principle and cylindrical mean curvature flows
Richard H. Bamler, Yi Lai
We introduce a new approach for analyzing ancient solutions and singularities of mean curvature flow that are locally modeled on a cylinder. Its key ingredient is a general mechani…
Classification of ancient cylindrical mean curvature flows and the Mean Convex Neighborhood Conjecture
Richard H. Bamler, Yi Lai
We resolve the Mean Convex Neighborhood Conjecture for mean curvature flows in all dimensions and for all types of cylindrical singularities. Specifically, we show that if the tang…
Convergence of Ricci flow and long-time existence of Harmonic map heat flow
Kyeongsu Choi, Yi Lai
For an ancient Ricci flow asymptotic to a compact integrable shrinker, or a Ricci flow developing a finite-time singularity modelled on the shrinker, we establish the long-time exi…
3-Manifolds with positive scalar curvature and bounded geometry
Otis Chodosh, Yi Lai, Kai Xu
We show that a complete contractible 3-manifold with positive scalar curvature and bounded geometry must be . We also show that an open handlebody of genus larger than…