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Journal Article
GENUS MINIMAL k -NOIDS AND SADDLE TOWERS IN
2023
Overview
For each$k\\geq 3$, we construct a$1$-parameter family of complete properly Alexandrov-embedded minimal surfaces in the Riemannian product space$\\mathbb {H}^2\\times \\mathbb {R}$with genus$1$and k embedded ends asymptotic to vertical planes. We also obtain complete minimal surfaces with genus$1$and$2k$ends in the quotient of$\\mathbb {H}^2\\times \\mathbb {R}$by an arbitrary vertical translation. They all have dihedral symmetry with respect to k vertical planes, as well as finite total curvature$-4k\\pi $. Finally, we provide examples of complete properly Alexandrov-embedded minimal surfaces with finite total curvature with genus$1$in quotients of$\\mathbb {H}^2\\times \\mathbb {R}$by the action of a hyperbolic or parabolic translation.
Publisher
Cambridge University Press
Subject
