Weighted Hamiltonian stationary Lagrangian submanifolds and generalized Lagrangian mean curvature flows in toric almost Calabi-Yau manifolds

Abstract

In this paper we generalize examples of Hamiltonian stationary Lagrangian submanifolds constructed by Lee and Wang in ${\mathbb{C}}^m$ to toric almost Calabi-Yau manifolds. We construct examples of weighted Hamiltonian stationary Lagrangian submanifolds in toric almost Calabi-Yau manifolds and solutions of generalized Lagrangian mean curvature flows starting from these examples. We allow these flows to have some singularities and topological changes.

16 pages

References in corpus (1)

• Hamiltonian minimal Lagrangian submanifolds in toric varieties