Tohoku Mathematical Journal

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

Hikaru Yamamoto

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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

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

Keywords
Lagrangian mean curvature flow special Lagrangian submanifold

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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