## Tohoku Mathematical Journal 2016 September SECOND SERIES VOL. 68, NO. 3

 Tohoku Math. J. 68 (2016), 329-347

Title WEIGHTED HAMILTONIAN STATIONARY LAGRANGIAN SUBMANIFOLDS AND GENERALIZED LAGRANGIAN MEAN CURVATURE FLOWS IN TORIC ALMOST CALABI--YAU MANIFOLDS

Author Hikaru Yamamoto

(Received April 22, 2014, revised October 24, 2014)
Abstract. In this paper, we generalize examples of Lagrangian mean curvature flows constructed by Lee and Wang in \$\mathbb{C}^m\$ to toric almost Calabi--Yau manifolds. To be more precise, 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.

Mathematics Subject Classification. Primary 53C42; Secondary 53C44.

Key words and phrases. Lagrangian mean curvature flow, special Lagrangian submanifold.