5 papers
A non-Kähler expanding Ricci soliton with a Kähler tangent cone at infinity
Richard H. Bamler, Eric Chen, Ronan J. Conlon
We construct an example of an asymptotically conical (AC) non-Kähler expanding gradient Ricci soliton that has a Kähler tangent cone at infinity. This yields an example of a Käh…
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…
Degree theory for 4-dimensional asymptotically conical gradient expanding solitons
Richard H. Bamler, Eric Chen
We develop a new degree theory for 4-dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymp…
On the Multiplicity One Conjecture for Mean Curvature Flows of surfaces
Richard H Bamler, Bruce Kleiner
We prove the Multiplicity One Conjecture for mean curvature flows of surfaces in . Specifically, we show that any blow-up limit of such mean curvature flows has multi…