论文标题
复杂的投影平面中的拉格朗日平均曲率流
Lagrangian mean curvature flow in the complex projective plane
论文作者
论文摘要
我们证明了托马斯 - 单调拉格朗日托里（Lagrangian Tori）的YAU-type猜想，可满足复杂的投影平面$ \ mathbb {cp}^2 $的对称条件。我们表明，在拉格朗日平均曲率流中，有史以来一直存在这种摩托学，最多只接受有限的手术手术，然后在无限时间流到最小的克利福德圆环。此外，我们表明我们可以在收敛之前构建具有任何有限数量的手术的圆环。在此过程中，我们证明了许多有趣的子公司结果，并开发了方法，这些方法对于研究了非卡拉比 - YAU歧管的拉格朗日平均曲率流也应该有用，即使在非对称情况下也是如此。
We prove a Thomas--Yau-type conjecture for monotone Lagrangian tori satisfying a symmetry condition in the complex projective plane $\mathbb{CP}^2$. We show that such tori exist for all time under Lagrangian mean curvature flow with surgery, undergoing at most a finite number of surgeries before flowing to a minimal Clifford torus in infinite time. Furthermore, we show that we can construct a torus with any finite number of surgeries before convergence. Along the way, we prove many interesting subsidiary results and develop methods which should be useful in studying Lagrangian mean curvature flow in non-Calabi--Yau manifolds, even in non-symmetric cases.
