Translating surfaces of the non-parametric mean curvature flow with prescribed contact angle

1994 ◽  
Vol 2 (1) ◽  
pp. 101-111 ◽  
Author(s):  
Steven J. Altschuler ◽  
Lang F. Wu
Keyword(s):  
Contact Angle ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Non Parametric

Translating spacelike graphs by mean curvature flow with prescribed contact angle

2014 ◽  
Vol 103 (6) ◽  
pp. 499-508 ◽  
Author(s):  
Shanze Gao ◽  
Guanghan Li ◽  
Chuanxi Wu
Keyword(s):  
Contact Angle ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow

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.

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