# Type-II singularities of two-convex immersed mean curvature flow

Geometric Flows (2016)

- Volume: 2, Issue: 1, page 143-161
- ISSN: 2353-3382

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topTheodora Bourni, and Mat Langford. "Type-II singularities of two-convex immersed mean curvature flow." Geometric Flows 2.1 (2016): 143-161. <http://eudml.org/doc/287125>.

@article{TheodoraBourni2016,

abstract = {We show that any strictly mean convex translator of dimension n ≥ 3 which admits a cylindrical estimate and a corresponding gradient estimate is rotationally symmetric. As a consequence, we deduce that any translating solution of the mean curvature flow which arises as a blow-up limit of a two-convex mean curvature flow of compact immersed hypersurfaces of dimension n ≥ 3 is rotationally symmetric. The proof is rather robust, and applies to a more general class of translator equations. As a particular application, we prove an analogous result for a class of flows of embedded hypersurfaces which includes the flow of twoconvex hypersurfaces by the two-harmonic mean curvature.},

author = {Theodora Bourni, Mat Langford},

journal = {Geometric Flows},

keywords = {rectifiable varifolds; boundary regularity; monotonicity formulae; boundaries},

language = {eng},

number = {1},

pages = {143-161},

title = {Type-II singularities of two-convex immersed mean curvature flow},

url = {http://eudml.org/doc/287125},

volume = {2},

year = {2016},

}

TY - JOUR

AU - Theodora Bourni

AU - Mat Langford

TI - Type-II singularities of two-convex immersed mean curvature flow

JO - Geometric Flows

PY - 2016

VL - 2

IS - 1

SP - 143

EP - 161

AB - We show that any strictly mean convex translator of dimension n ≥ 3 which admits a cylindrical estimate and a corresponding gradient estimate is rotationally symmetric. As a consequence, we deduce that any translating solution of the mean curvature flow which arises as a blow-up limit of a two-convex mean curvature flow of compact immersed hypersurfaces of dimension n ≥ 3 is rotationally symmetric. The proof is rather robust, and applies to a more general class of translator equations. As a particular application, we prove an analogous result for a class of flows of embedded hypersurfaces which includes the flow of twoconvex hypersurfaces by the two-harmonic mean curvature.

LA - eng

KW - rectifiable varifolds; boundary regularity; monotonicity formulae; boundaries

UR - http://eudml.org/doc/287125

ER -

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