A computed example of nonuniqueness of mean curvature flow in R3

S. Angenent, T. Ilmanen, D.L. Chopp

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Abstract

A family of surface (M{sub t}){sub t{element_of}R} in R{sup n} is said to be moving by mean curvature provided. Here H(x) is the mean curvature vector of M{sub t} at x. Is there a smooth hypersurface in some Euclidean space whose mean curvature flow admits nonuniqueness after the onset of singularities? In this note we present compelling numerical evidence for nonuniqueness starting from a certain smooth surface in R{sup 3}. In contrast to other references, we do not have a complete proof for our construction.
Original languageEnglish
Pages (from-to)1937-1958
JournalCommunications on Partial Differential Equations
Volume20
DOIs
StatePublished - 1995

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