Subsequent singularities in mean-convex mean curvature flow
By B. White. 2011
69 citations recorded by the source corpus.
We use Ilmanen’s elliptic regularization to prove that for an initially smooth mean convex hypersurface in $$\mathbf {R}^n$$Rn moving by mean curvature flow, the surface is very nearly convex in a spacetime neighborhood of every singularity. In particular, the tangent flows are all shrinking spheres or cylinders. Previously this was known only (1) for $$n\le 7$$n≤7, and (2) for arbitrary $$n$$n up to the first singular time.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/22e0ff709a7e6bc6289f6d204d0c7c1fd7706694
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Bruce Kleiner
- Robert Haslhofer
- Jeff Cheeger
- A. Naber
- Nicola Gigli
- G. Tian
- Richard Bamler
- Andrea Mondino
In Geometry and Topology
- Robert Haslhofer
- Bruce Kleiner
- A. Naber
- Jeff Cheeger
- G. Tian
- Richard Bamler
- Nicola Gigli
- Andrea Mondino
Citations in the corpus
- Mean Curvature Flow of Mean Convex Hypersurfaces (2013, methodology): “As in [36, 38, 40], our theorems can be viewed as results about the level set flow.”
- Quantitative Stratification and the Regularity of Mean Curvature Flow (2012, result): “Our results build upon the deep regularity theory of Brian White [9, 10, 11, 12], which we briefly recall now: Given a Brakke flow M = {(Mt, t)} he considered the stratification of the singular set S ⇢M, (3) S ⇢ S(1) ⇢ · · · ⇢ S ⇢ S , where by definition X = (x, t) 2 Sj if and only if no tangent flo”