In recent years symplectic geometry and symplectic topology have grown to large subbranches in mathematics and had a great impact on other areas in mathematics. When interested in geometry, a geometer always considers geometric structures that arise on immersed submanifolds. In symplectic geometry there is a distinguished class of immersions, known as Lagrangian submanifolds . In particular, minimal Lagrangian submanifolds, called special Lagrangians, are very important in mirror symmetry. Lagrangian mean curvature flow is an important example of Lagrangian deformation. From which we can get the special Lagrangian submanifolds. In recent years, there have been many papers about this subject and the result by K.Smoczyk and Mu-Tao Wang [WS] is very important and beautiful. Our main purpose in this article is to give a new proof for the main result in [WS] from the viewpoint of fully nonlinear partial differential equations.
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机译:近年来,辛几何和辛拓扑已发展为数学的大分支,并且对数学的其他领域产生了巨大影响。当对几何感兴趣时,几何学家总是考虑沉浸在子流形上的几何结构。在辛几何中,有一类特殊的浸没,称为拉格朗日子流形。特别是,最小拉格朗日子流形(称为特殊拉格朗日子)在镜像对称性中非常重要。拉格朗日平均曲率流是拉格朗日变形的重要例子。从中我们可以得到特殊的拉格朗日子流形。近年来,有关该主题的论文很多,K.Smoczyk和Mu-Tao Wang [WS]的结果非常重要且美观。本文的主要目的是从完全非线性偏微分方程的观点为[WS]中的主要结果提供新的证明。
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