## 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.

### MSC:

 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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