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

2014/08/01 by Koiso, Miyuki, Piccione, Paolo, Shoda, Toshihiro
#35J62 #53A10 #58E12 #58J55 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1408.0953

Abstract

We use bifurcation theory to determine the existence of infinitely many new examples of triply periodic minimal surfaces in \mathbb R³. These new examples form branches issuing from the H-family, the rPD-family, the tP-family, and the tD-family, that converge to some degenerate embedding of the families. As to nondegenerate triply periodic minimal surfaces, we prove a perturbation result using an equivariant implicit function theorem.

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