论文标题
自由边界CMC表面的间隙结果在共同欧几里得三球中
Gap results for free boundary CMC surfaces in conformally Euclidean three-balls
论文作者
论文摘要
在这项工作中，我们将$ m =（\ mathbb {b}^3_r，\ bar {g}）$作为欧几里得三球，配备了公制$ \ bar {g} = e^{g} = e^{2H} \ left \ left \ weft \ langle，\ right \ rangle $ unclorm ycuclormal of euclidean metrid euclidean。 We show that if a free boundary CMC surface $Σ$ in $M$ satisfies a pinching condition on the length of the traceless second fundamental tensor which involves the support function of $Σ$, the positional conformal vector field $\vec{x}$ and its potential function $σ,$ then either $Σ$ is a disk or $Σ$ is an annulus rotationally symmetric.在特定情况下，我们构建了一个最小表面的示例，当$ m $是高斯空间时，以严格的凸边界为$ m $，这说明了我们的结果。这些结果扩展到CMC病例，并向许多其他不同的共同欧几里得空间扩展到Haizhong Li和Changwei Xiong获得的主要结果。
In this work, we consider $M=(\mathbb{B}^3_r,\bar{g})$ as the Euclidean three-ball with radius $r$ equipped with the metric $\bar{g}=e^{2h}\left\langle , \right\rangle$ conformal to the Euclidean metric. We show that if a free boundary CMC surface $Σ$ in $M$ satisfies a pinching condition on the length of the traceless second fundamental tensor which involves the support function of $Σ$, the positional conformal vector field $\vec{x}$ and its potential function $σ,$ then either $Σ$ is a disk or $Σ$ is an annulus rotationally symmetric. In a particular case, we construct an example of minimal surface with strictly convex boundary in $M$, when $M$ is the Gaussian space, that illustrate our results. These results extend to the CMC case and to many others different conformally Euclidean spaces the main result obtained by Haizhong Li and Changwei Xiong.
