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New minimal surfaces in \({\mathbb {S}}^3\) desingularizing the Clifford tori

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Abstract

For each integer \(m\ge 2\) and \(\ell \ge 1\) we construct a pair of compact embedded minimal surfaces of genus \(1+ 4m(m-1)\ell \). These surfaces desingularize the m Clifford tori meeting each other along a great circle at the angle of \(\pi /m\). They are invariant under a finite group of screw motions and have no reflection symmetry across a great sphere.

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Acknowledgments

Jaigyoung Choe is supported in part by NRF, 2011-0030044, SRC-GAIA.

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Authors and Affiliations

  1. Korea Institute for Advanced Study, Seoul, 130-722, Korea

    Jaigyoung Choe

  2. Département de Mathématiques, Université F. Rabelais, 37200, Tours, France

    Marc Soret

Authors
  1. Jaigyoung Choe
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  2. Marc Soret
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Correspondence to Jaigyoung Choe.

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In memory of Professor Hyo Chul Myung, former president of KIAS.

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Choe, J., Soret, M. New minimal surfaces in \({\mathbb {S}}^3\) desingularizing the Clifford tori. Math. Ann. 364, 763–776 (2016). https://doi.org/10.1007/s00208-015-1239-3

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  • DOI: https://doi.org/10.1007/s00208-015-1239-3

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