Kummer K3曲面中的拉格朗日平均曲率流
Lagrangian mean curvature flow in the Kummer K3 surface
AI总结：
本文在Kummer K3曲面中构造了收敛到特殊拉格朗日球面的拉格朗日平均曲率流新例子，通过标量扰动和不动点论证解决。
AI中文摘要：
几何分析中的一个主要问题是理解拉格朗日平均曲率流的行为。这已被证明是一个具有挑战性的问题，特别是，已知的能够对所有时间存在并收敛到极小拉格朗日的流的显式例子并不多。在本文中，我们在Kummer K3曲面中构造了收敛到特殊拉格朗日球面的拉格朗日平均曲率流的新例子。我们将构造归结为一个标量扰动问题，该问题可通过不动点论证求解。
英文摘要：
A major problem in geometric analysis is to understand the behaviour of the Lagrangian mean curvature flow. This has proved to be a challenging problem, in particular, not many explicit examples of flows that exist for all time and converge to a minimal Lagrangian are known. In this paper we construct new examples of Lagrangian mean curvature flows in the Kummer K3 surface that converge to special Lagrangian spheres. We reduce the construction to a scalar perturbation problem that can be solved by a fixed point argument.
