scholarly journals Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space

2016 ◽  
Vol 165 (4) ◽  
pp. 723-791 ◽  
Author(s):  
Roland Donninger ◽  
Joachim Krieger ◽  
Jérémie Szeftel ◽  
Willie Wong
Keyword(s):  
Minkowski Space ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Codimension One

scholarly journals Generalized hyperbolic mean curvature flow in Minkowski space $R^{1,1}$

2020 ◽  
Author(s):  
Zenggui Wang ◽  
Xiuzhan Li
Keyword(s):  
Life Span ◽  
Minkowski Space ◽  
Hyperbolic System ◽  
Finite Time ◽  
Mean Curvature ◽  
Initial Velocity ◽  
Mean Curvature Flow ◽  
Small Variation ◽  
Curvature Flow ◽  
Quasilinear Hyperbolic System

This paper concerns the generalized hyperbolic mean curvature flow for spacelike curves in Minkowski $R^{1,1}$. Base on the derived quasilinear hyperbolic system, we investigate the formation of singularities in the motion of these curves. In particular, under the generalized hyperbolic mean curvature flow, we prove that the motion of periodic spacelike curves with small variation on one period and small initial velocity blows up in finite time. Some blowup results have been obtained and the estimates on the life-span of the solutions are given.

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