We prove a bubble tree convergence theorem for a sequence of closed Hamiltonian stationary Lagrangian surfaces with bounded areas and Willmore energies in a complete Kähler surface. We also prove two strong compactness theorems on the space of Hamiltonian stationary Lagrangian tori in \({\mathbb {C}}^2\) and \({{\mathbb {C}}}{{\mathbb {P}}}^2\) respectively.

中文翻译：

---

关于Kähler曲面中哈密顿平稳拉格朗日曲面的紧致性

我们证明了完整的Kähler曲面中带边界区域和Willmore能量的闭合哈密顿平稳拉格朗日曲面序列的气泡树收敛定理。我们还证明了\（{\ mathbb {C}} ^ 2 \）和\（{{\ mathbb {C}}} {{\ mathbb {P}}}中的哈密顿平稳拉格朗日托里空间上的两个强紧致性定理^ 2 \）。