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arXiv · 1408.0953

On bifurcation and local rigidity of triply periodic minimal surfaces in $\mathbb R^3$

Miyuki Koiso·Paolo Piccione·Toshihiro Shoda
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Abstract

We use bifurcation theory to determine the existence of infinitely many new examples of triply periodic minimal surfaces in $\mathbb R^3$. 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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Miyuki Koiso, Paolo Piccione, Toshihiro Shoda. 2014-08-01. On bifurcation and local rigidity of triply periodic minimal surfaces in $\mathbb R^3$. https://arxiv.org/abs/1408.0953

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