Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 3658
Articles: 2'599'751
Articles rated: 2609

02 November 2024
 
  » arxiv » arxiv.0707.0239

 Article overview



Hamiltonian Stationary Shrinkers and Expanders for Lagrangian Mean Curvature Flows
Yng-Ing Lee ; Mu-Tao Wang ;
Date 2 Jul 2007
AbstractWe construct examples of shrinkers and expanders for Lagrangian mean curvature flows. These examples are Hamiltonian stationary and asymptotic to the union of two Hamiltonian stationary cones found by Schoen and Wolfson. The Schoen-Wolfson cones $C_{p,q}$ are obstructions to the existence problems of special Lagrangians or Lagrangian minimal surfaces in the variational approach. It is known that these cone singularities cannot be resolved by any smooth oriented Lagrangian submanifolds. The shrinkers and expanders that we found can be glued together to yield solutions of the Brakke motion-a weak formulation of the mean curvature flow. For any coprime pair $(p,q)$ other than $(2,1)$, we construct such a solution that resolves any single Schoen-Wolfson cone $C_{p,q}$. This thus provides an evidence to Schoen-Wolfson’s conjecture that the $(2,1)$ cone is the only area-minimizing cone. Higher dimensional generalizations are also obtained.
Source arXiv, arxiv.0707.0239
Services Forum | Review | PDF | Favorites   
 
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
important:
of broad interest:
readable:
new:
correct:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.






ScienXe.org
» my Online CV
» Free

home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2024 - Scimetrica