Mean curvature flow with a forcing term in minkowski space

2005 ◽  
Vol 25 (2) ◽  
pp. 205-246 ◽  
Author(s):  
Mark A. S. Aarons
Keyword(s):  
Minkowski Space ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Forcing Term

NUMERICAL EVIDENCE OF FATTENING FOR THE MEAN CURVATURE FLOW

1996 ◽  
Vol 06 (06) ◽  
pp. 793-813 ◽  
Author(s):  
FRANCESCA FIERRO ◽  
MAURIZIO PAOLINI
Keyword(s):  
Numerical Simulations ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Normal Direction ◽  
Compact Surface ◽  
Principal Curvatures ◽  
Forcing Term ◽  
The Mean ◽  
Motion By Mean Curvature

In this paper we describe some numerical simulations in the context of mean curvature flow. We recover a few different approaches in modeling the evolution of an interface Σ which evolves according to the law: V=κ+g where V is the velocity in the inward normal direction, κ is the sum of the principal curvatures and g is a given forcing term. We will discuss about the phenomenon of fattening or nonuniqueness of the solution, recalling what is known about this subject. Finally we show some interesting numerical simulations that suggest evidence of fattening starting from different initial interfaces. Of particular interest is the result obtained for a torus in ℝ4 which would be a first example of a regular and compact surface showing evidence of fattening in the case of pure motion by mean curvature (no forcing term).

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.

Sign in / Sign up

Export Citation Format

Share Document