发表机构
Fudan University（复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究Ricci-flat Kähler流形中具有单值相位的Hamiltonian stationary Lagrangian流，建立了相位与平均曲率的关系，推导了几乎单调性公式、Allard型正则性定理及极限结构，并应用于复欧几里得空间中该流的正则性与刚性。
AI 中文摘要
本文研究了Ricci-flat Kähler流形的开子集中具有单值相位的Hamiltonian stationary Lagrangian流。我们首先在Ricci-flat Kähler流形中建立了一类积分Lagrangian流的相位与平均曲率之间的关系。然后，我们推导了具有单值调和相位的积分Lagrangian流的几个基本性质，包括一个几乎单调性公式、一个Allard型正则性定理，以及该类中流的极限结构。最后，我们将上述结果应用于研究复欧几里得空间中在特定条件下的Hamiltonian stationary Lagrangian图的正则性和刚性。
英文摘要
In this paper, we investigate Hamiltonian stationary Lagrangian currents with single-valued phases in open sets of Ricci-flat Kähler manifolds. We first establish the relation between phase and mean curvature for a class of integral Lagrangian currents in Ricci-flat Kähler manifolds. Then we derive several fundamental properties of integral Lagrangian currents with single-valued harmonic phases, including an almost monotonicity formula, an Allard-type regularity theorem, and the structure of limits of currents in this class. Finally, we apply the above results to study the regularity and rigidity of Hamiltonian stationary Lagrangian graphs in complex Euclidean space under certain conditions.
Comments53 pages
