Stability of triply periodic minimal surfaces |
| |
Affiliation: | 1. Department of Mathematics, Meijo University, Tempaku, Nagoya 468-8502, Japan;2. Faculty of Education, Saga University, 1 Honjo-machi, Saga-city, Saga, 840-8502, Japan |
| |
Abstract: | 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. |
| |
Keywords: | Minimal surfaces Flat tori Stability Morse index |
本文献已被 ScienceDirect 等数据库收录! |
|