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Mean curvature flow with surgeries

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Mean Curvature Flow and Isoperimetric Inequalities

Part of the book series: Advanced Courses in Mathematics — CRM Barcelona ((ACMBIRK))

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Abstract

In this section we describe the mean curvature flow with surgeries which has been defined in [48] for two-convex surfaces of dimension n ≥ 3. Such a construction is inspired by the one which was introduced by Hamilton [37] for the Ricci flow and which enabled Perelman [56] to prove the geometrization conjecture for three-dimensional manifolds.

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Authors and Affiliations

  1. Departamento de Geometría y Topología Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Manuel Ritoré

  2. Dipartimento di Matematica, Università di Roma “Tor Vergata” Via della Ricerca Scientifica, 00133, Roma, Italy

    Carlo Sinestrari

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  1. Manuel Ritoré
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Ritoré, M., Sinestrari, C. (2010). Mean curvature flow with surgeries. In: Mean Curvature Flow and Isoperimetric Inequalities. Advanced Courses in Mathematics — CRM Barcelona. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0213-6_11

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