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On the Existence and Uniqueness of Ancient Rescaled Mean Curvature Flows (2212.10798v1)
Published 21 Dec 2022 in math.DG and math.AP
Abstract: We show existence of ancient solutions to the rescaled mean curvature flow starting from a given asymptotically conical self-expander. These are examples of mean curvature flows coming out of cones that are not self-similar. We also show a strong uniqueness theorem when the cone is generic and use it to classify mean curvature flows coming out of generic cones of small entropy in low dimensions.