scholarly journals Mean Curvature Flow of Mean Convex Hypersurfaces

2016 ◽  
Vol 70 (3) ◽  
pp. 511-546 ◽  
Author(s):  
Robert Haslhofer ◽  
Bruce Kleiner
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Mean Convex ◽  
Convex Hypersurfaces

scholarly journals A survey on Inverse mean curvature flow in ROSSes

2017 ◽  
Vol 4 (1) ◽  
pp. 245-262
Author(s):  
Giuseppe Pipoli
Keyword(s):  
Mean Curvature ◽  
Symmetric Spaces ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Unified Approach ◽  
Inverse Mean Curvature Flow ◽  
Rank One ◽  
Similarities And Differences ◽  
Mean Convex ◽  
Convex Hypersurfaces

AbstractIn this survey we discuss the evolution by inverse mean curvature flow of star-shaped mean convex hypersurfaces in non-compact rank one symmetric spaces. We show similarities and differences between the case considered, with particular attention to how the geometry of the ambient manifolds influences the behaviour of the evolution. Moreover we try, when possible, to give an unified approach to the results present in literature.

scholarly journals Mean curvature flow with surgeries of two–convex hypersurfaces

2008 ◽  
Vol 175 (1) ◽  
pp. 137-221 ◽  
Author(s):  
Gerhard Huisken ◽  
Carlo Sinestrari
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Convex Hypersurfaces

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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