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

Miyuki Koiso, Paolo Piccione, Toshihiro Shoda

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)2743-2778
Number of pages36
JournalAnnales de l'Institut Fourier
Volume68
Issue number6
DOIs
Publication statusPublished - Jan 1 2018

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All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology

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