Stability of triply periodic minimal surfaces
| Autor: | Norio Ejiri, Toshihiro Shoda |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Surface (mathematics)
Pure mathematics Minimal surface Euclidean space 010102 general mathematics 01 natural sciences Stability (probability) Computational Theory and Mathematics 0103 physical sciences 010307 mathematical physics Geometry and Topology 0101 mathematics Triply periodic minimal surface Analysis Mathematics Gyroid |
| Zdroj: | Differential Geometry and its Applications. 67:101555 |
| ISSN: | 0926-2245 |
| DOI: | 10.1016/j.difgeo.2019.101555 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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