论文标题
Lagrangian卷的较低半持续点
Lower semi-continuity of Lagrangian volume
论文作者
论文摘要
我们研究了相对于Hofer-和$γ$ distance的一类单调Lagrangian Submanifolds Hamiltonian同位素相互相对于彼此的HOFER-和$γ$ distance的较低的封闭拉格朗日歧管的表面积，即表面积的较低。我们证明，在两种情况下，体积为$γ$ - 半连续。在第一个中，音量形式来自带有大量哈密顿等异构体的Kähler指标，但在拉格朗日submanifold上没有其他约束。第二个是相对于任何兼容度量的卷，但拉格朗日submanifold必须是圆环。结果，在这两种情况下，体积都是较低的半连续。
We study lower semi-continuity properties of the volume, i.e., the surface area, of a closed Lagrangian manifold with respect to the Hofer- and $γ$-distance on a class of monotone Lagrangian submanifolds Hamiltonian isotopic to each other. We prove that volume is $γ$-lower semi-continuous in two cases. In the first one the volume form comes from a Kähler metric with a large group of Hamiltonian isometries, but there are no additional constraints on the Lagrangian submanifold. The second one is when the volume is taken with respect to any compatible metric, but the Lagrangian submanifold must be a torus. As a consequence, in both cases, the volume is Hofer lower semi-continuous.
