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A singular example for the averaged mean curvature flow. (English) Zbl 0982.53061

It has been conjectured for quite some time that the averaged mean curvature flow can drive embedded plane curves to a loss of embeddedness; such a conjecture enters the literature with M. Gage [Contemp. Math. 51, 51-62 (1986; Zbl 0608.53002)].
In the present paper, using numerical experiments, the author presents an embedded curve in the two-dimensional Euclidean space which, under the averaged mean curvature flow, develops first a self-intersection and then a singularity of blowup type for the curvature, all in finite time.

MSC:

53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
53A04 Curves in Euclidean and related spaces

Citations:

Zbl 0608.53002
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References:

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