Ginzburg–Landau Vortex and Mean Curvature Flow with External Force Field

2006 ◽  
Vol 22 (6) ◽  
pp. 1831-1842 ◽  
Author(s):  
Huai Yu Jian ◽  
Yan Nan Liu
Keyword(s):  
Force Field ◽  
External Force ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Ginzburg Landau ◽  
External Force Field

Evolution of Spacelike Hypersurfaces by Mean Curvature Minus External Force Field in Minkowski Space

2009 ◽  
Vol 9 (3) ◽  
Author(s):  
Yannan Liu ◽  
Huaiyu Jian
Keyword(s):  
Force Field ◽  
Minkowski Space ◽  
External Force ◽  
Mean Curvature ◽  
Spacelike Hypersurface ◽  
Spacelike Surface ◽  
Convexity Condition ◽  
External Force Field ◽  
Spacelike Hypersurfaces

AbstractWe study the evolution of spacelike hypersurface moving by mean curvature minus an external force field in Minkowski space. It is shown that the flow will exist for all time if the initial spacelike surface has two compact spacelike barrier surfaces and the external force field satisfies a weak convexity condition.

scholarly journals Evolution of the first eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow

2020 ◽  
Vol 18 (1) ◽  
pp. 1518-1530
Author(s):  
Xuesen Qi ◽  
Ximin Liu
Keyword(s):  
Laplace Operator ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Second Fundamental Form ◽  
Coefficient Function ◽  
First Eigenvalue ◽  
Initial Hypersurface ◽  
The Mean ◽  
The Laplace Operator

Abstract In this paper, we discuss the monotonicity of the first nonzero eigenvalue of the Laplace operator and the p-Laplace operator under a forced mean curvature flow (MCF). By imposing conditions associated with the mean curvature of the initial hypersurface and the coefficient function of the forcing term of a forced MCF, and some special pinching conditions on the second fundamental form of the initial hypersurface, we prove that the first nonzero closed eigenvalues of the Laplace operator and the p-Laplace operator are monotonic under the forced MCF, respectively, which partially generalize Mao and Zhao’s work. Moreover, we give an example to specify applications of conclusions obtained above.

scholarly journals Mean curvature flow with free boundary outside a hypersphere

2017 ◽  
Vol 369 (12) ◽  
pp. 8319-8342 ◽  
Author(s):  
Glen Wheeler ◽  
Valentina-Mira Wheeler
Keyword(s):  
Free Boundary ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow
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