Hamiltonian Stationary Shrinkers and Expanders for Lagrangian Mean Curvature Flows

Simple item page
dc.creatorLee, Yng-Ing
dc.creatorWang, Mu-Tao
dc.date2007-07-02
dc.date.accessioned2026-07-07T08:13:33Z
dc.date.available2026-07-07T08:13:33Z
dc.descriptionWe 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.
dc.description19 pages
dc.identifierhttps://arxiv.org/abs/0707.0239
dc.identifierhttp://arxiv.org/abs/0707.0239
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132806
dc.subjectDifferential Geometry
dc.subject53C40
dc.titleHamiltonian Stationary Shrinkers and Expanders for Lagrangian Mean Curvature Flows
dc.typetext

Files

Collections

arXiv