Mean curvature flow with surgery. (English) Zbl 1370.53046

The general aim of the interesting paper under review is to give a new proof for the existence of mean curvature flow with surgery for \(2\)-convex hypersurfaces in \(\mathbb{R}^N,\) working for all \(N\geq3.\) The authors’ main focus is on shortness, brevity and simplicity. Moreover, the proofs work for mean convex surfaces in \(\mathbb{R}^3,\) which was left as an open problem after [G. Huisken and C. Sinestrari, Invent. Math. 175, No. 1, 137–221 (2009; Zbl 1170.53042)]. Furthermore, anticipating future applications, the authors derive a priori estimates in a completely local and very flexible setting.


53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
35K93 Quasilinear parabolic equations with mean curvature operator
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces


Zbl 1170.53042
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