论文标题
在Fraser-Sargent型最小表面的索引上
On the Index of Fraser-Sargent-type minimal surfaces
论文作者
论文摘要
弗雷泽 - 萨金表面是四维单元欧几里得球中的自由边界最小表面。它们无限地延长了欧几里得空间中浸入的最小表面。在本文中，我们计算了莫尔斯指数和这些扩展最小表面的无效。球外面的这些表面的部分是外部自由边界最小表面。我们提供了数值证据，表明它们是稳定的。作为这些结果的推论，我们在球内弗雷泽 - 萨金表面的指数上获得了一个下限。获得的下限并不锋利。我们提供计算实验，并陈述有关改进指数下限的猜想。与之无关，我们还发现了球内弗雷泽 - 萨金表面的索引上的上限。
Fraser-Sargent surfaces are free boundary minimal surfaces in the four-dimensional unit Euclidean ball. Extended infinitely they define immersed minimal surfaces in the Euclidean space. In the present paper we compute the Morse index and the nullity of these extended minimal surfaces. The parts of these surfaces outside the ball are exterior free boundary minimal surfaces. We provide a numerical evidence that they are stable. As a corollary of these results we obtain a lower bound on the index of Fraser-Sargent surfaces inside the ball. The obtained lower bound is not sharp. We provide computational experiments and state a conjecture about an improved index lower bound. Independently of it we also find an upper bound on the index of Fraser-Sargent surfaces inside the ball.
