AI 中文总结
该研究在特定假设下证明了$\boldsymbol{\text{C}}^3$中带有横截二重极点的紧浸入特殊拉格朗日链的特殊拉格朗日切锥的唯一性，核心方法基于离散Lojasiewicz型不等式，源于胶合障碍机制。
AI 中文摘要
在光滑雅可比场可积性及链的相交模式条件假设下，我们证明了$\boldsymbol{\text{C}}^3$中特殊拉格朗日切锥的唯一性，这类切锥的链是带有横截二重极点的紧浸入特殊拉格朗日曲面。证明基于离散Lojasiewicz型不等式，该不等式源于胶合障碍机制。
英文摘要
Under the assumption of integrability of the smooth Jacobi fields and a condition on the intersection pattern of the link, we prove uniqueness of special Lagrangian tangent cones in $\mathbb{C}^3$ whose links are compact immersed special Legendrian surfaces with transverse double points. The proof is based on a discrete Lojasiewicz type inequality, which comes from a gluing obstruction mechanism.
Comments30 pages
