A computed example of nonuniqueness of mean curvature flow in R{sup 3}

Journal Article · Sun Dec 31 04:00:00 EST 1995 · Communications in Partial Differential Equations

DOI:https://doi.org/10.1080/03605309508821158· OSTI ID:482475

Angenent, S; Ilmanen, T ^[1]; Chopp, D L ^[2]

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1. Univ. of Wisconsin, Madison, WI (United States)
2. Univ. of Washington, Seattle, WA (United States)

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.

• Sponsoring Organization: USDOE
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 482475
• Journal Information: Communications in Partial Differential Equations, Journal Name: Communications in Partial Differential Equations Journal Issue: 11-12 Vol. 20; ISSN 0360-5302; ISSN CPDIDZ
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
EUCLIDEAN SPACE
MATHEMATICAL MANIFOLDS
PARTIAL DIFFERENTIAL EQUATIONS
RIEMANN SPACE
SURFACES