We construct many self-similar and translating solitons for Lagrangian mean curvature flow, including self-expanders and translating solitons with arbitrarily small oscillation on the Lagrangian angle. Our translating solitons play the same role as cigar solitons in Ricci flow, and are important in studying the regularity of Lagrangian mean curvature flow. Given two transverse Lagrangian planes ?~n in ?~n with sum of characteristic angles less than π, we show there exists a Lagrangian self-expander asymptotic to this pair of planes. The Maslov class of these self-expanders is zero. Thus they can serve as local models for surgeries on Lagrangian mean curvature flow. Families of self-shrinkers and self-expanders with different topologies are also constructed. This paper generalizes the work of Anciaux [1], Joyce [12], Lawlor [15], and Lee and Wang [18, 19].
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机译：我们为拉格朗日平均曲率流构造了许多自相似的平移孤子，包括自扩张器和在拉格朗日角上任意小的振荡的平移孤子。我们的平移孤子在Ricci流中的作用与雪茄孤子相同，对研究拉格朗日平均曲率流的规律性很重要。给定两个横向拉格朗日平面？〜n在？〜n中，特征角的总和小于π，我们证明了这对平面存在一个拉格朗日自展开器渐近线。这些自扩展器的Maslov类为零。因此，它们可以用作拉格朗日平均曲率流手术的局部模型。还构建了具有不同拓扑的自收缩器和自扩展器的族。本文概括了Anciaux [1]，Joyce [12]，Lawlor [15]以及Lee and Wang [18，19]的工作。
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