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math.DG2025
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…
math.DG2025
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…