scholarly journals Stability of the surface area preserving mean curvature flow in Euclidean space

2015 ◽  
Vol 106 (3) ◽  
pp. 483-501 ◽  
Author(s):  
Zheng Huang ◽  
Longzhi Lin
Keyword(s):  
Euclidean Space ◽  
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

scholarly journals Complete Self-Shrinking Solutions for Lagrangian Mean Curvature Flow in Pseudo-Euclidean Space

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Ruiwei Xu ◽  
Linfen Cao
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Indefinite Metric ◽  
Bernstein Theorem ◽  
Strictly Convex ◽  
Convex Solution

Letf(x)be a smooth strictly convex solution ofdet(∂2f/∂xi∂xj)=exp(1/2)∑i=1nxi(∂f/∂xi)-fdefined on a domainΩ⊂Rn; then the graphM∇fof∇fis a space-like self-shrinker of mean curvature flow in Pseudo-Euclidean spaceRn2nwith the indefinite metric∑dxidyi. In this paper, we prove a Bernstein theorem for complete self-shrinkers. As a corollary, we obtain if the Lagrangian graphM∇fis complete inRn2nand passes through the origin then it is flat.

scholarly journals Rigidity results and topology at infinity of translating solitons of the mean curvature flow

2017 ◽  
Vol 19 (06) ◽  
pp. 1750002 ◽  
Author(s):  
Debora Impera ◽  
Michele Rimoldi
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Minimal Hypersurfaces ◽  
Rigidity Results ◽  
And Topology ◽  
The Mean ◽  
Translating Solitons

In this paper, we obtain rigidity results and obstructions on the topology at infinity of translating solitons of the mean curvature flow in the Euclidean space. Our approach relies on the theory of [Formula: see text]-minimal hypersurfaces.

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