Saddle towers with infinitely many ends

Laurent Mazet (1) , M. Magdalena Rodriguez (2) , Martin Traizet (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We prove the existence of nonperiodic, properly embedded minimal surfaces in $\mathbb{R}^2\times\mathbb{S}^1$ with genus zero, infinitely many ends and one limit end (in particular, they have infinite total curvature).

Domaines: Géométrie différentielle [math.DG]

Laurent Mazet, M. Magdalena Rodriguez, Martin Traizet. Saddle towers with infinitely many ends. Indiana University Mathematics Journal, 2007, 56 (6), pp.2821--2838. ⟨hal-00118104⟩