论文标题
欧几里得球中任何拓扑类型的自由边界最小表面通过形状优化
Free boundary minimal surfaces of any topological type in Euclidean balls via shape optimization
论文作者
论文摘要
对于任何紧凑的表面$σ$，具有光滑，非空边界，我们将自由边界最小浸入欧几里得球$ \ mathbb {b}^n $中，其中$ n $由$σ$的拓扑控制。对于第一个非平凡的steklov特征值，我们将其作为最大化的指标。我们的主要技术结果涉及对特征值的渐近控制，这使我们能够证明其余的光谱差距条件可以完成弗雷泽（Fraser） - 乔恩（Schoen）和第二名的作者，以获取此类Mazimigitization指标。我们的施工从第一位命名作者的早期工作中引起了Siffert的动力，涉及封闭情况下的相应问题。
For any compact surface $Σ$ with smooth, non-empty boundary, we construct a free boundary minimal immersion into a Euclidean Ball $\mathbb{B}^N$ where $N$ is controlled in terms of the topology of $Σ$. We obtain these as maximizing metrics for the isoperimetric problem for the first non-trivial Steklov eigenvalue. Our main technical result concerns asymptotic control on eigenvalues in a delicate glueing construction which allows us to prove the remaining spectral gap conditions to complete the program by Fraser--Schoen and the second named author to obtain such mazimizing metrics. Our construction draws motivation from earlier work by the first named author with Siffert on the corresponding problem in the closed case.
