Entire self-similar solutions to Lagrangian Mean curvature flow

Details Entire self-similar solutions to Lagrangian Mean curvature flow Entire self-similar solutions to Lagrangian Mean curvature flow

2009-05-24

arxiv.org/abs/0905.3869v1

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.

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