Translating Solitons in a Lorentzian Setting, Submersions and Cohomogeneity One Actions

具有对称性的 $\mathbb{C}^m$ 中的拉格朗日平移孤立子与特殊拉格朗日子流形

Lagrangian Translating Solitons and Special Lagrangians in $\mathbb{C}^m$ with Symmetries

本文在具有对称性的 $\mathbb{C}^m$ 中构造了新的拉格朗日平移孤立子和特殊拉格朗日子流形，推广了 Castro-Lerma 的 Ansatz，并对单群情形给出完整分类，同时描述了关于非紧子群对称的余齐性一例子。

余一性拉格朗日平均曲率流

Cohomogeneity-One Lagrangian Mean Curvature Flow

本文研究余一性拉格朗日平均曲率流，分类自相似解与特殊拉格朗日子流形，刻画奇点爆破模型，并给出无穷多新孤子与奇点模型例子。

Translating solitons from semi-Riemannian foliations

We recall the notion of (vertical) translating solitons in a product of a semi-Riemannian manifold $(M,g)$ and the real line. Mainly, we restrict our attention to those which are the graph of a smooth function. When dealing with submersions, we show a criteria to lift (or project) translating solitons from the base manifold to the total space (or viceversa). In particular, manifolds foliated by codimension 1 orbits of a Lie group action give rise to such solitons, up to solving a first-order ordinary differential equation. This gives us explicit criteria under which the graph of a function is …