Stationary solutions of an area-preserving curvature flow in an inhomogeneous medium

2021 ◽  
Author(s):  
R. Lui ◽  
H. Ninomiya
Keyword(s):  
Inhomogeneous Medium ◽  
Curvature Flow ◽  
Stationary Solutions ◽  
Area Preserving

On an area-preserving inverse curvature flow of convex closed plane curves

2021 ◽  
Vol 280 (8) ◽  
pp. 108931
Author(s):  
Laiyuan Gao ◽  
Shengliang Pan ◽  
Dong-Ho Tsai
Keyword(s):  
Curvature Flow ◽  
Plane Curves ◽  
Area Preserving ◽  
Closed Plane

scholarly journals Nonlinear stability of stationary solutions for curvature flow with triple junction

2009 ◽  
Vol 38 (4) ◽  
pp. 721-769 ◽  
Author(s):  
Harald GARCKE ◽  
Yoshihito KOHSAKA ◽  
Daniel ŠEVČOVIČ
Keyword(s):  
Nonlinear Stability ◽  
Triple Junction ◽  
Curvature Flow ◽  
Stationary Solutions

Evolution of non-simple closed curves in the area-preserving curvature flow

2017 ◽  
Vol 148 (3) ◽  
pp. 659-668 ◽  
Author(s):  
Xiao-Liu Wang ◽  
Wei-Feng Wo ◽  
Ming Yang
Keyword(s):  
Global Solution ◽  
Blow Up ◽  
Curvature Flow ◽  
Convex Curve ◽  
Closed Curves ◽  
Area Preserving ◽  
Locally Convex

The convergence and blow-up results are established for the evolution of non-simple closed curves in an area-preserving curvature flow. It is shown that the global solution starting from a locally convex curve converges to an m-fold circle if the enclosed algebraic area A0 is positive, and evolves into a point if A0 = 0.

The Surface Area Preserving Mean Curvature Flow in Quasi-Fuchsian Manifolds

2012 ◽  
Vol 32 (6) ◽  
pp. 2191-2202 ◽  
Author(s):  
Tian Daping ◽  
Li Guanghan ◽  
Wu Chuanxi
Keyword(s):  
Surface Area ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Area Preserving

scholarly journals Pulsating wave for mean curvature flow in inhomogeneous medium

2008 ◽  
Vol 19 (6) ◽  
pp. 661-699 ◽  
Author(s):  
N. DIRR ◽  
G. KARALI ◽  
N. K. YIP
Keyword(s):  
Inhomogeneous Medium ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Lipschitz Continuity ◽  
Curvature Flow ◽  
Periodic Forcing ◽  
Gradient Bounds ◽  
Speed Of Propagation ◽  
Reference Hyperplane ◽  
Effective Speed

We prove the existence and uniqueness of pulsating waves for the motion by mean curvature of an n-dimensional hypersurface in an inhomogeneous medium, represented by a periodic forcing. The main difficulty is caused by the degeneracy of the equation and the fact the forcing is allowed to change sign. Under the assumption of weak inhomogeneity, we obtain uniform oscillation and gradient bounds so that the evolving surface can be written as a graph over a reference hyperplane. The existence of an effective speed of propagation is established for any normal direction. We further prove the Lipschitz continuity of the speed with respect to the normal and various stability properties of the pulsating wave. The results are related to the homogenisation of mean curvature flow with forcing.

scholarly journals On a planar area-preserving curvature flow

2012 ◽  
Vol 141 (5) ◽  
pp. 1783-1789 ◽  
Author(s):  
Xiao-Li Chao ◽  
Xiao-Ran Ling ◽  
Xiao-Liu Wang
Keyword(s):  
Curvature Flow ◽  
Planar Area ◽  
Area Preserving
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