On bifurcation and local rigidity of triply periodic minimal surfaces in ℝ3

Miyuki Koiso, Paolo Piccione, Toshihiro Shoda

研究成果: Contribution to journalArticle査読

4 被引用数 (Scopus)

抄録

We study the space of triply periodic minimal surfaces in ℝ3, giving a result on the local rigidity and a result on the existence of bifurcation. We prove that, near a triply periodic minimal surface with nullity three, the space of triply periodic minimal surfaces consists of a smooth five-parameter family of pairwise non-homothetic surfaces. On the other hand, if there is a smooth oneparameter family of triply periodic minimal surfaces {Xt}t containing X0 where the Morse index jumps by an odd integer, it will be proved the existence of a bifurcating branch issuing from X0. We also apply these results to several known examples.

本文言語英語
ページ(範囲)2743-2778
ページ数36
ジャーナルAnnales de l'Institut Fourier
68
6
DOI
出版ステータス出版済み - 2018

All Science Journal Classification (ASJC) codes

  • 代数と数論
  • 幾何学とトポロジー

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