Convergent sequences of closed minimal surfaces embedded in $\S 3$

Abstract

given two minimal surfaces embedded in $\S 3$ of genus $g$ we prove the existence of a sequence of non-congruent compact minimal surfaces embedded in $\S 3$ 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.

arXiv comment19 pages, typo in Lemma B.1 corrected, statement in Remark 4.1 rephrased, proof of Theorem 2.2 enhanced, additional commentary in final remarks

References in corpus (1)

• A proof of the Lawson conjecture for minimal tori embedded in $\S 3$