Year: 2024
Type: article
Abstract: We construct two different families of properly Alexandrov-immersed surfaces in \mathbb{H}^{2}\times \mathbb{R} with constant mean curvature 0 , genus one and k\geq2 ends ( k=2 only for one of these families). These ends are asymptotic to vertical H -cylinders for 0 . This shows that there is not a Schoen-type theorem for immersed surfaces with positive constant mean curvature in \mathbb{H}^{2}\times\mathbb{R} . These surfaces are obtained by means of a conjugate construction.
DOI: 10.4171/rmi/1536
Authors: Jesús Castro-Infantes, José S. Santiago
Institutions: Universidad Politécnica de Madrid, Universidad de Jaén
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404547207