On the genus of triply periodic minimal surfaces

Martin Traizet (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We prove the existence of embedded minimal surfaces of arbitrary genus at least 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.

Domaines: Géométrie différentielle [math.DG]

Martin Traizet. On the genus of triply periodic minimal surfaces. Journal of Differential Geometry, 2008, 79, pp.243--275. ⟨hal-00281610⟩