Adding one handle to half-plane layers

Laurent Mazet (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

In this paper, we build properly embedded singly periodic minimal surfaces which have infinite total curvature in the quotient by the period. These surfaces are constructed by adding a handle to the toroidal half-plane layers defined by H. Karcher. The technics that use is to solve a Jenkins-Serrin problem over a strip domain and to consider the conjugate minimal surface to the graph.

Domaines: Géométrie différentielle [math.DG]

Laurent Mazet. Adding one handle to half-plane layers. Journal of Differential Geometry, 2010, 84 (2), pp.389--407. ⟨hal-00082699⟩