Entire self-similar solutions to Lagrangian Mean curvature flow

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dc.creatorChau, Albert
dc.creatorChen, Jingyi
dc.creatorHe, Weiyong
dc.date2009-05-24
dc.date.accessioned2026-07-07T13:17:50Z
dc.date.available2026-07-07T13:17:50Z
dc.descriptionWe 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.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/0905.3869
dc.identifierhttp://arxiv.org/abs/0905.3869
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/231246
dc.subjectDifferential Geometry
dc.subject53C44; 53A10
dc.titleEntire self-similar solutions to Lagrangian Mean curvature flow
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