论文标题
$ {\ Mathbb {l}}}^{4} $和三个Weierstrass表示形式的边缘被困的表面
Marginally trapped surfaces in ${\mathbb{L}}^{4}$ and three Weierstrass representations
论文作者
论文摘要
我们构建了新的可集成系统，以呈现空格表面的Weierstrass类型表示形式，其平均曲率向量$ \ Mathbf {h} $满足无效条件$ \ langle \ langle \ langle \ mathbf {h}，\ Mathbf {h} \ rangle = 0 $ {\ mathbb {l}}}^{4} $。我们的新WeierStrass演示文稿同时扩展了在$ {\ Mathbb {\ Mathbb {l}}^{3} $中的最大表面的同时（第一类和第二种），并在$ {\ Mathbb {\ Mathbb {\ Mathbb {\ Mathbb {r}}}}^{3} $中延长了最大表面。我们求解了一个线性部分不同方程，以构建边缘捕获的表面的明确示例，而无处消失的平均曲率向量。
We construct new integrable systems to present Weierstrass type representations for spacelike surfaces whose mean curvature vector $\mathbf{H}$ satisfies the null condition $\langle \mathbf{H}, \mathbf{H} \rangle=0$ in the four dimensional Lorentz-Minkowski space ${\mathbb{L}}^{4}$. Our new Weierstrass presentations extend simultaneously classical Weierstrass representations (of the first kind and the second kind) for maximal surfaces in ${\mathbb{L}}^{3}$ and minimal surfaces in ${\mathbb{R}}^{3}$. We solve a linear partial differental equation to construct explicit examples of marginally trapped surfaces with nowhere vanishing mean curvature vector.
