scholarly journals The surface area preserving mean curvature flow

2003 ◽  
Vol 7 (1) ◽  
pp. 7-30 ◽  
Author(s):  
James McCoy
Keyword(s):  
Surface Area ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Area Preserving

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

The dynamics of drops and attached interfaces for the constrained Allen–Cahn equation

2001 ◽  
Vol 12 (1) ◽  
pp. 1-24 ◽  
Author(s):  
D. STAFFORD ◽  
M. J. WARD ◽  
B. WETTON
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Asymptotic Result ◽  
Interface Motion ◽  
Front Tracking Method ◽  
Cahn Equation ◽  
Area Preserving ◽  
Dimensional Domain

The motion of interfaces for a mass-conserving Allen–Cahn equation that are attached to the boundary of a two-dimensional domain is studied. In the limit of thin interfaces, the interface motion for this problem is known to be governed by an area-preserving mean curvature flow. A numerical front-tracking method, that allows for a numerical solution of this type of curvature flow, is used to compute the motion of interfaces that are attached orthogonally to the boundary. Results obtained from these computations are favourably compared with a previously-derived asymptotic result for the motion of attached interfaces that enclose a small area. The area-preserving mean curvature flow predicts that a semi-circular interface is stationary when it is attached to a flat segment of the boundary. For this case, the interface motion is shown to be metastable and an explicit characterization of the metastability is given.

scholarly journals Superresolution of Images Using Area Preserving Geometric Evolution Laws

2012 ◽  
Vol 2012 ◽  
pp. 1-5
Author(s):  
Caroline Jäger ◽  
Simon Praetorius ◽  
Axel Voigt
Keyword(s):  
Level Set ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Small Scale ◽  
Geometric Evolution ◽  
Flow Surface ◽  
Willmore Flow ◽  
Evolution Laws ◽  
Area Preserving

PDE-based approaches are used to obtain superresolution of images. Using level set method for area constraint geometric evolution laws allows to remove pixelation in images without removing small-scale features. We compare mean curvature flow, surface diffusion, and Willmore flow for this purpose.

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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