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

Mayer, Uwe F.

Exp. Math. 10, No. 1, 103-107 (2001).

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.

Reviewer: Jose Carmelo Gonzalez-Davila (La Laguna)

MSC:

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

Keywords:

blowup of curvature; averaged mean curvature flow; curve; self-intersection; singularity

Citations:

Zbl 0608.53002

References:

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