Non-periodic Riemann examples with handles

Filippo Morabito (1) , Martin Traizet (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We show the existence of 1-parameter families of non-periodic, complete, embedded minimal surfaces in Euclidean space with infinitely many parallel planar ends. In particular we are able to produce finite genus examples and quasi-periodic examples of infinite genus.

Domaines: Géométrie différentielle [math.DG]

Filippo Morabito, Martin Traizet. Non-periodic Riemann examples with handles. Advances in Mathematics, 2012, 229, pp.26--53. ⟨hal-00785185⟩