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

Theodora 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 -