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On the genus of triply periodic minimal surfaces

Martin Traizet Laboratoire de Math´ematiques et de Physique Th´eorique

Differential Geometry mathscidoc:1609.10070

Journal of Differential Geometry, 79, (2), 243-275, 2008
We prove the existence of embedded minimal surfaces of arbitrary genus g ≥ 3 in any flat 3-torus. In fact, we construct a sequence of such surfaces converging to a planar foliation of the 3-torus. In particular, the area of the surface can be chosen arbitrarily large.
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@inproceedings{martin2008on,
  title={ON THE GENUS OF TRIPLY PERIODIC MINIMAL SURFACES},
  author={Martin Traizet},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909132241930464727},
  booktitle={Journal of Differential Geometry},
  volume={79},
  number={2},
  pages={243-275},
  year={2008},
}
Martin Traizet. ON THE GENUS OF TRIPLY PERIODIC MINIMAL SURFACES. 2008. Vol. 79. In Journal of Differential Geometry. pp.243-275. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909132241930464727.
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