发表机构
University of Notre Dame; Stanford University（圣母大学; 斯坦福大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将Caffarelli-Hardt-Simon扰动论证推广到特殊拉格朗日量领域，证明正则特殊拉格朗日锥的桥接原理，进而得到具有多个给定孤立锥形奇点的特殊拉格朗日子流形的存在性。
AI 中文摘要
我们将截断正则极小锥的Caffarelli-Hardt-Simon扰动论证推广到特殊拉格朗日量框架中，并遵循Nathan Smale的思路证明了正则特殊拉格朗日锥的桥接原理。该桥接原理给出了带有给定正则切锥的锥形奇异特殊拉格朗日子流形的一般存在定理：对于$\boldsymbol{\text{C}}^m$中具有相同拉格朗日角且适当排列的任意有限个此类锥，存在一个带边界的连通特殊拉格朗日子流形，其奇点处的切锥恰好是给定的锥。特别地，我们在$\boldsymbol{\text{C}}^m$中得到了带有多个给定孤立锥形奇点的新特殊拉格朗日子流形。
英文摘要
We extend the Caffarelli-Hardt-Simon perturbation argument for truncated regular minimal cones to the special Lagrangian setting and prove a bridge principle for regular special Lagrangian cones in the spirit of Nathan Smale. Our bridge principle yields a general existence theorem for conically singular special Lagrangian submanifolds with prescribed regular tangent cones: for any finite list of such cones in $\mathbb C^m$ having the same Lagrangian angle and suitably arranged, there exists a connected special Lagrangian submanifold with boundary and isolated conical singularities whose tangent cones at its singularities are precisely the prescribed cones. When applied to the graphical special Lagrangian cone in $\mathbb{C}^5$ recently discovered by Bhattacharya, Orriols, and Skorobogatova, we obtain infinite families of $C^{1,1}$ viscosity solutions to the special Lagrangian equation having any finite number of isolated singularities.
Comments36 pages. Comments are welcome! v2: We added Corollary 1, in which we apply the main theorem to prove the existence of solutions to the special Lagrangian equation with multiple isolated singularities
