No mass drop for mean curvature flow of mean convex hypersurfaces
A possible evolution of a compact hypersurface in R n + 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 equal...
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| Veröffentlicht in: | Duke mathematical journal 2008-04, Vol.142 (2), p.283-312 |
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| container_title | Duke mathematical journal |
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| creator | Metzger, Jan Schulze, Felix |
| description | A possible evolution of a compact hypersurface in R n + 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 |
| doi_str_mv | 10.1215/00127094-2008-007 |
| format | Article |
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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. 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| identifier | ISSN: 0012-7094 |
| ispartof | Duke mathematical journal, 2008-04, Vol.142 (2), p.283-312 |
| issn | 0012-7094 1547-7398 |
| language | eng |
| recordid | cdi_projecteuclid_primary_oai_CULeuclid_euclid_dmj_1206642156 |
| source | Project Euclid Complete |
| subjects | 49Q20 53C44 etc. Geometric evolution equations (mean curvature flow Ricci flow Variational problems in a geometric measure-theoretic setting |
| title | No mass drop for mean curvature flow of mean convex hypersurfaces |
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