论文标题
特殊的拉格朗日织带
Special Lagrangian webbing
论文作者
论文摘要
我们在一般的Calabi-yau歧管中建造了横向马斯洛夫指数$ 0 $ 0 $ 0 $或$ n $交点点附近的假想特殊拉格朗日圆柱的家族。因此，我们获得了此类交叉点附近的开放式拉格朗日亚曼菲尔德的大地测量学。此外，这一结果是迈向非扰动构造的封闭阳性拉格朗日亚曼菲尔德大地测量学的第一步。另外，我们介绍了一种证明$ c^{1,1} $在非平滑基因座上的阳性拉格朗日人的定期。该方法用于表明$ c^{1,1} $阳性球形的大地测量在端点的小扰动下持续存在，从而提高了作者先前结果的规律性。特别是，我们获得了$ c^{1,1} $解决方案的第一个示例，该示例是在任意尺寸中的正lagrangian Geodesic方程中的第一个示例，这些方程并非在等法下不变。一路走来，我们研究了复杂矢量空间中阳性拉格朗日线性子空间的测量学，并在整个论文中证明了Maslov索引$ 0 $ 0 $或$n。$的先验存在，这是作者先前的作品中引入的圆柱变换。
We construct families of imaginary special Lagrangian cylinders near transverse Maslov index $0$ or $n$ intersection points of positive Lagrangian submanifolds in a general Calabi-Yau manifold. Hence, we obtain geodesics of open positive Lagrangian submanifolds near such intersection points. Moreover, this result is a first step toward the non-perturbative construction of geodesics of closed positive Lagrangian submanifolds. Also, we introduce a method for proving $C^{1,1}$ regularity of geodesics of positive Lagrangians at the non-smooth locus. This method is used to show that $C^{1,1}$ geodesics of positive Lagrangian spheres persist under small perturbations of endpoints, improving the regularity of a previous result of the authors. In particular, we obtain the first examples of $C^{1,1}$ solutions to the positive Lagrangian geodesic equation in arbitrary dimension that are not invariant under isometries. Along the way, we study geodesics of positive Lagrangian linear subspaces in a complex vector space, and prove an a priori existence result in the case of Maslov index $0$ or $n.$ Throughout the paper, the cylindrical transform introduced in previous work of the authors plays a key role.
