论文标题
最小的拉格朗日摩尔和动作角度坐标
Minimal Lagrangian tori and action-angle coordinates
论文作者
论文摘要
我们调查了哪些$ n $维圆环动作的轨道在$ 2N $二维的折叠式福利kähler歧管$ m $中很少。换句话说，我们研究了最小的亚曼福尔德，这些submanifolds似乎是矩形kähler歧管上的瞬间图的纤维。在其他问题中，我们调查并给出部分答案：（1）存在多少这种Lagrangian Tori？ （2）仅仅从环境几何形状来表征它们的稳定性，作为区域功能的临界点吗？ （3）鉴于感谢您的旋转歧管（对于哪一组轨道$ s $），是否有兼容的感谢您的Kähler指标，其最小的Lagrangian Orbits集为$ S $？
We investigate which orbits of an $n$-dimensional torus action on a $2n$-dimensional toric Kähler manifold $M$ are minimal. In other words, we study minimal submanifolds appearing as the fibres of the moment map on a toric Kähler 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 $S$, is there a compatible toric Kähler metric whose set of minimal Lagrangian orbits is $S$?
