论文标题
有限的熵在平板中翻译孤子
Finite entropy translating solitons in slabs
论文作者
论文摘要
我们研究了平均曲率流的孤子，$σ^2 \ subseteq \ mathbb {r}^3 $包含在平板中，并且具有有限的属和有限的熵。作为我们结果的第一个结果，我们可以列举切片的连接组件来定义渐近不变的$ω^\ pm（σ）最终将熵量化为整数步骤，将机翼数量的概念与莫尔斯理论相结合，以最小的表面，我们证明，如果$σ$是一个完整的嵌入式孤子，将slab包含在平板中的孤独感和熵$λ（σ）= 3 $，然后包含垂直$σ$σ$σ$σ$σ，
We study translating solitons for the mean curvature flow, $Σ^2\subseteq\mathbb{R}^3$ which are contained in slabs, and are of finite genus and finite entropy. As a first consequence of our results, we can enumerate connected components of slices to define asymptotic invariants $ω^\pm(Σ)\in\mathbb{N}$, which count the numbers of "wings''. Analyzing these, we give a method for computing the entropies $λ(Σ)$ via a simple formula involving the wing numbers, which in particular shows that for this class of solitons the entropy is quantized into integer steps. Finally, combining the concept of wing numbers with Morse theory for minimal surfaces, we prove the uniqueness theorem that if $Σ$ is a complete embedded simply connected translating soliton contained in a slab with entropy $λ(Σ)=3$ and containing a vertical line, then $Σ$ is one of the translating pitchforks of Hoffman-Martín-White
