A mountain-pass theorem for asymptotically conical self-expanders

Published 30 Mar 2020 in math.DG and math.AP | (2003.13857v1)

Abstract: We develop a min-max theory for asymptotically conical self-expanders of mean curvature flow. In particular, we show that given two distinct strictly stable self-expanders that are asymptotic to the same cone and bound a domain, there exists a new asymptotically conical self-expander trapped between the two.

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