Abstract
We have seen in Chapter 7 that, if ∂E is smooth and compact, then for short times there exists a unique smooth compact mean curvature flow starting from ∂E. We have also seen in Example 3.21 that the sphere of radius R 0 shrinks to a point in the finite time R 0 2/(2(n — 1)). This time can be interpreted as a singularity time of the flow, even if the evolving shere reduces to a point. In this chapter we describe an example, due to Grayson [159], of a smooth compact mean curvature flow in ℝ3 which develops a singularity, and does not reduce to a point at the same time: this example and the proof that we present here follows that of [159]. In [126] the reader can find various differences in the proof.
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© 2013 Scuola Normale Superiore Pisa
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Bellettini, G. (2013). Grayson’s example. In: Lecture Notes on Mean Curvature Flow, Barriers and Singular Perturbations. Publications of the Scuola Normale Superiore, vol 12. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-429-8_8
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DOI: https://doi.org/10.1007/978-88-7642-429-8_8
Publisher Name: Edizioni della Normale, Pisa
Print ISBN: 978-88-7642-428-1
Online ISBN: 978-88-7642-429-8
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