Noncollapsing in mean-convex mean curvature flow

By Ben Andrews. 2012

146 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8939975d8b9822de7f453c8d3ab012d1f6fe5b82

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Moduli of continuity, isoperimetric profiles, and multi-point estimates in geometric heat equations (2014, result): “The non-collapsing estimate for mean curvature flow in [1] is somewhat analogous to that for the heat equation in the previous section.”
EMBEDDED CONSTANT MEAN CURVATURE TORI IN THE THREE-SPHERE (2012, methodology): “We recall here some of the expressions which arise from this picture (see also the discussion in [3] and [4]).”
Embedded minimal tori in S3 and the Lawson conjecture (2012, methodology): “The argument in [2] relies in a crucial way on the positivity of the mean curvature; in particular, the argument is not applicable in the case of minimal surfaces.”
The singular set of mean curvature flow with generic singularities (2014, background): “Moreover, if the initial hypersurface is mean convex, then all singularities are cylindrical; see [3,27,30–33,48,49,53].”
Ancient solutions of the mean curvature flow (2013, unknown): “H ≥ 0) mean curvature flows satisfying the conclusion of Andrews’ beautiful noncollapsing result [2], see also White [23] and Sheng-Wang [21].”
Unique asymptotics of ancient convex mean curvature flow solutions (2015, background): “Andrews [1] introduced the following notion of “non-collapsedness” for any compact mean convex subset K ⊂ R.”
Mean curvature flow with surgery (2014, methodology): “Our new approach to surgery is motivated by our paper [HK13a], where we gave a streamlined treatment of White’s theory of mean convex level set (Brakke) flow [Whi00, Whi03, Whi11], based on the beautiful noncollapsing result of Andrews [And12]: Given any α > 0, the”
Convex ancient solutions of the mean curvature flow (2014, background): “Remark 5.5 An important class of solutions satisfying (5.13) are the ones satisfying the following noncollapsing property of Andrews [2]: there exists α > 0 such that for every point p ∈ Mt we can find a ball of radius α/H(p, t) which is enclosed by Mt and touches Mt from inside at p.”
Mean Curvature Flow of Mean Convex Hypersurfaces (2013, methodology): “We recently gave a new treatment of this theory [7], based on the beautiful non-collapsing result of Andrews [8].”
Uniqueness of the bowl soliton (2014, background): “In general, a very important feature of blowup limits of a mean-convex mean curvature flow is that they are always noncollapsed; see White [26], Sheng and Wang [22], Andrews [2] and Haslhofer and Kleiner [12].”