Mathematics – Differential Geometry
Scientific paper
2009-05-24
Mathematics
Differential Geometry
9 pages
Scientific paper
We consider self-similar solutions to mean curvature evolution of entire Lagrangian graphs. When the Hessian of the potential function $u$ has eigenvalues strictly uniformly between -1 and 1, we show that on the potential level all the shrinking solitons are quadratic polynomials while the expanding solitons are in one-to-one correspondence to functions of homogenous of degree 2 with the Hessian bound. We also show that if the initial potential function is cone-like at infinity then the scaled flow converges to an expanding soliton as time goes to infinity.
Chau Albert
Chen Jingyi
He Weiyong
No associations
LandOfFree
Entire self-similar solutions to Lagrangian Mean curvature flow does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Entire self-similar solutions to Lagrangian Mean curvature flow, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Entire self-similar solutions to Lagrangian Mean curvature flow will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-114876