Convergent sequences of closed minimal surfaces embedded in $\S3$

Details Convergent sequences of closed minimal surfaces embedded in $\S3$ Convergent sequences of closed minimal surfaces embedded in $\S3$

2009-12-30

arxiv.org/abs/0912.5519v2

Mathematics

Differential Geometry

19 pages, typo in Lemma B.1 corrected, statement in Remark 4.1 rephrased, proof of Theorem 2.2 enhanced, additional commentary

Scientific paper

given two minimal surfaces embedded in $\S3$ of genus $g$ we prove the existence of a sequence of non-congruent compact minimal surfaces embedded in $\S3$ of genus $g$ that converges in $C^{2,\alpha}$ to a compact embedded minimal surface provided some conditions are satisfied. These conditions also imply that, if any of these two surfaces is embedded by the first eigenvalue, so is the other.

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