Compact translating solitons with non-empty planar boundary
Compact translating solitons with non-empty planar boundary
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DOI：
10.1016/j.difgeo.2016.03.003
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发表时间：
2016-08
影响因子：
0.5
通讯作者：
Juncheol Pyo
中科院分区：
文献类型：
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作者：
Juncheol Pyo
本文研究了具有非空平面边界的紧致平移孤子。每个边界分量位于与平移方向正交的平面中。首先证明了当平面边界为圆或凸且平移孤子以常角与包含边界的平面相交时，紧平移孤子是整个旋转对称严格凸图形曲面的一部分.其次，我们证明了跨越两条水平平面Jordan曲线的紧致平移孤子继承了其边界的对称性。我们还给出了具有平面边界的紧致平移孤子的平衡型公式。
In this paper, we consider compact translating solitons with non-empty planar boundary. Each boundary component lies in a plane which is orthogonal to the translating direction. We firstly prove that when the planar boundary is either a circle or convex and the translating soliton meets the plane containing the boundary with a constant angle, then the compact translating soliton is part of an entire rotationally symmetric strictly convex graphical surface. Secondly, we show that a compact translating soliton spanning two horizontal planar Jordan curves inherits the symmetries of its boundary. We also show a balancing type formula for compact translating solitons with planar boundary.