Stability of triply periodic minimal surfaces
Stability of triply periodic minimal surfaces
复制标题
三周期最小曲面的稳定性
DOI：
10.1016/j.difgeo.2019.101555
复制
发表时间：
2019
影响因子：
0.5
通讯作者：
Shoda Toshihiro
中科院分区：
文献类型：
--
作者：
Ejiri Norio;Shoda Toshihiro
1992年，Ross证明了三维欧氏空间中的一些经典的三重周期极小曲面（施瓦茨P曲面、D曲面和Schoen回转面）对于保体积变分是稳定的。本文将这一结果推广到四个单参数三重周期极小曲面族，即tP族，tD族，rPD族和H族.得到了保体积稳定的充分条件，并作为数值应用，证明了对于每一类极小曲面，每个莫尔斯指标为1的三重周期极小曲面都是保体积稳定的.
In 1992, Ross proved that some classical triply periodic minimal surfaces in three-dimensional Euclidean space (Schwarz P surface, D surface, and Schoen's gyroid) are stable for volume-preserving variations. This paper extends the result to four one-parameter families of triply periodic minimal surfaces, namely, tP family, tD family, rPD family, and H family. We obtain sufficient conditions for volume-preserving stability, and as their numerical applications, we prove that, for each family, every triply periodic minimal surface with Morse index one is volume-preserving stable.