Behaviour of singularities of the rotationally symmetric, volume-preserving mean curvature flow

2003 ◽  
Vol 17 (1) ◽  
pp. 1-16 ◽  
Author(s):  
M. Athanassenas
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Rotationally Symmetric ◽  
Volume Preserving

The Effective Dynamics of the Volume Preserving Mean Curvature Flow

2018 ◽  
Vol 172 (2) ◽  
pp. 458-476
Author(s):  
Ilias Chenn ◽  
G. Fournodavlos ◽  
I. M. Sigal
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Effective Dynamics ◽  
Volume Preserving

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

2016 ◽  
Vol 2 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Theodora Bourni ◽  
Mat Langford
Keyword(s):  
Mean Curvature ◽  
General Class ◽  
Mean Curvature Flow ◽  
Blow Up ◽  
Analogous Result ◽  
Curvature Flow ◽  
Type Ii ◽  
Rotationally Symmetric ◽  
The Mean ◽  
Mean Convex

AbstractWe 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.

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