Duke Mathematical Journal

No mass drop for mean curvature flow of mean convex hypersurfaces

Jan Metzger and Felix Schulze

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Abstract

A possible evolution of a compact hypersurface in Rn+1 by mean curvature past singularities is defined via the level set flow. In the case where the initial hypersurface has positive mean curvature, we show that the Brakke flow associated to the level set flow is actually a Brakke flow with equality. As a consequence, we obtain the fact that no mass drop can occur along such a flow. A further application of the techniques used above is to give a new variational formulation for mean curvature flow of mean convex hypersurfaces

Article information

Source
Duke Math. J., Volume 142, Number 2 (2008), 283-312.

Dates
First available in Project Euclid: 27 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1206642156

Digital Object Identifier
doi:10.1215/00127094-2008-007

Mathematical Reviews number (MathSciNet)
MR2401622

Zentralblatt MATH identifier
1136.53051

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 49Q20: Variational problems in a geometric measure-theoretic setting

Citation

Metzger, Jan; Schulze, Felix. No mass drop for mean curvature flow of mean convex hypersurfaces. Duke Math. J. 142 (2008), no. 2, 283--312. doi:10.1215/00127094-2008-007. https://projecteuclid.org/euclid.dmj/1206642156


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