Duke Mathematical Journal

Mean curvature flow with surgery

Robert Haslhofer and Bruce Kleiner

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We give a new proof for the existence of mean curvature flow with surgery of 2-convex hypersurfaces in RN. Our proof works for all N3, including mean convex surfaces in R3. We also derive a priori estimates for a more general class of flows in a local and flexible setting.

Article information

Duke Math. J., Volume 166, Number 9 (2017), 1591-1626.

Received: 27 July 2015
Revised: 22 September 2016
First available in Project Euclid: 23 February 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 35K93: Quasilinear parabolic equations with mean curvature operator 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

mean curvature flow formation of singularities $2$-convex surgery


Haslhofer, Robert; Kleiner, Bruce. Mean curvature flow with surgery. Duke Math. J. 166 (2017), no. 9, 1591--1626. doi:10.1215/00127094-0000008X. https://projecteuclid.org/euclid.dmj/1487818918

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