scholarly journals Volume-preserving mean curvature flow for tubes in rank one symmetric spaces of non-compact type

2017 ◽  
Vol 56 (3) ◽  
Author(s):  
Naoyuki Koike
Keyword(s):  
Mean Curvature ◽  
Symmetric Spaces ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Compact Type ◽  
Rank One ◽  
Volume Preserving

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.

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
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