Minimal Lagrangian tori and action-angle coordinates
Differential Geometry
2020-05-01 v1 Symplectic Geometry
Abstract
We investigate which orbits of an -dimensional torus action on a -dimensional toric K\"ahler manifold are minimal. In other words, we study minimal submanifolds appearing as the fibres of the moment map on a toric K\"ahler manifold. Amongst other questions we investigate and give partial answers to the following: (1) How many such minimal Lagrangian tori exist? (2) Can their stability, as critical points of the area functional, be characterised just from the ambient geometry? (3) Given a toric symplectic manifold, for which sets of orbits , is there a compatible toric K\"ahler metric whose set of minimal Lagrangian orbits is ?
Cite
@article{arxiv.2004.14697,
title = {Minimal Lagrangian tori and action-angle coordinates},
author = {Gonçalo Oliveira and Rosa Sena-Dias},
journal= {arXiv preprint arXiv:2004.14697},
year = {2020}
}