scholarly journals The volume-preserving mean curvature flow in Euclidean space

2009 ◽  
Vol 243 (2) ◽  
pp. 331-355 ◽  
Author(s):  
Haozhao Li
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Volume Preserving

The Effective Dynamics of the Volume Preserving Mean Curvature Flow

2018 ◽  
Vol 172 (2) ◽  
pp. 458-476
Author(s):  
Ilias Chenn ◽  
G. Fournodavlos ◽  
I. M. Sigal
Keyword(s):  
Mean Curvature ◽  
Mean Curvature Flow ◽  
Curvature Flow ◽  
Effective Dynamics ◽  
Volume 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.

Sign in / Sign up

Export Citation Format

Share Document