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Minimal surfaces in the 3-sphere by stac...
Wiygul, David...

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Minimal surfaces in the 3-sphere by stacking Clifford tori by Wiygul, David ( Author )
Lemonjar Open Access
N.A
26-02-2015
Extending work of Kapouleas and Yang, for any integers N≥2, k,ℓ≥1, and m sufficiently large, we apply gluing methods to construct in the round 3-sphere a closed embedded minimal surface that has genus kℓm2(N−1)+1 and is invariant under a Dkm×Dℓm subgroup of O(4), where Dn is the dihedral group of order 2n. Each such surface resembles the union of N nested topological tori, all small perturbations of a single Clifford torus T, that have been connected by kℓm2(N−1) small catenoidal tunnels, with kℓm2 tunnels joining each pair of neighboring tori. In the large-m limit for fixed N, k, and ℓ, the corresponding surfaces converge to T counted with multiplicity N.
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Article
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36.88 KB
English
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MYR 0.01
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doi:10.4310/jdg/1583377214
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