Surfaces with constant mean curvature 1/2 and genus one in H2xR

TL;DR

This paper introduces a new family of constant mean curvature 1/2 surfaces in hyperbolic space cross real line, characterized by genus one, multiple ends, and dihedral symmetry, expanding the known examples in differential geometry.

Contribution

It constructs novel constant mean curvature surfaces in H2xR with specific topological and symmetry properties, derived as sister surfaces of Plateau solutions.

Findings

Surfaces are Alexandrov-embedded.

Existence of a family with k ends, genus 1, and k-fold dihedral symmetry.

Surfaces have constant mean curvature 1/2 in H2xR.

Abstract

We construct new constant mean curvature surfaces in H2xR. They arise as sister surfaces of Plateau solutions. It is a family of MC 1/2 surfaces with k ends, genus 1 and k-fold dihedral symmetry, k greater 2. The surfaces are Alexandrov- embedded.