Genus one -surfaces with -ends in
Jesús Castro-Infantes
Universidad Politécnica de Madrid, Madrid, SpainJosé S. Santiago
Universidad de Jaén, Jaén, Spain
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Abstract
We construct two different families of properly Alexandrov-immersed surfaces in with constant mean curvature , genus one and ends ( only for one of these families). These ends are asymptotic to vertical -cylinders for . This shows that there is not a Schoen-type theorem for immersed surfaces with positive constant mean curvature in . These surfaces are obtained by means of a conjugate construction.
Cite this article
Jesús Castro-Infantes, José S. Santiago, Genus one -surfaces with -ends in . Rev. Mat. Iberoam. 41 (2025), no. 1, pp. 365–400
DOI 10.4171/RMI/1536