## Tohoku Mathematical Journal

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

Hikaru Yamamoto

#### 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.

#### Article information

Source
Tohoku Math. J. (2), Volume 68, Number 3 (2016), 329-347.

Dates
Received: 22 April 2014
Revised: 24 October 2014
First available in Project Euclid: 23 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1474652263

Digital Object Identifier
doi:10.2748/tmj/1474652263

Mathematical Reviews number (MathSciNet)
MR3550923

Zentralblatt MATH identifier
1361.53052

#### Citation

Yamamoto, Hikaru. Weighted Hamiltonian stationary Lagrangian submanifolds and generalized Lagrangian mean curvature flows in toric almost Calabi-Yau manifolds. Tohoku Math. J. (2) 68 (2016), no. 3, 329--347. doi:10.2748/tmj/1474652263. https://projecteuclid.org/euclid.tmj/1474652263

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