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Mean curvature flow with surgery of mean convex surfaces in \(\mathbb {R}^3\)

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Abstract

We define a notion of mean curvature flow with surgery for two-dimensional surfaces in \(\mathbb {R}^3\) with positive mean curvature. Our construction relies on the earlier work of Huisken and Sinestrari in the higher dimensional case. One of the main ingredients in the proof is a new estimate for the inscribed radius established by the first author (Invent Math, 2015).

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Notes

  1. See [19], pp. 189–190, for the definition of \(\hat{\mathcal {P}}(p_0,t_0,L_0+4,2\theta _0)\).

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Simon Brendle

  2. Mathematisches Institut, Universität Tübingen, 72076, Tübingen, Germany

    Gerhard Huisken

Authors
  1. Simon Brendle
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  2. Gerhard Huisken
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Correspondence to Simon Brendle.

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Brendle, S., Huisken, G. Mean curvature flow with surgery of mean convex surfaces in \(\mathbb {R}^3\) . Invent. math. 203, 615–654 (2016). https://doi.org/10.1007/s00222-015-0599-3

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  • DOI: https://doi.org/10.1007/s00222-015-0599-3

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