Entire constant mean curvature graphs in ℍ2 × ℝ

For $0 \leq H < \frac{1}{2}$ , we construct entire $H$ -graphs in $ℍ^{2} \times ℝ$ that are parabolic and not invariant by one parameter groups of isometries of $ℍ^{2} \times ℝ$ . Their asymptotic boundaries are $(\partial_{\infty} ℍ^{2}) \times ℝ$ ; they are dense at infinity. Previously, the only known examples of entire $H$ -graphs, $0 < H < \frac{1}{2}$ , were conformally hyperbolic invariant surfaces. When $H = 0$ , the examples are minimal graphs constructed by P. Collin and the second author.

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Keywords

entire graphs, constant mean curvature, parabolic

Mathematical Subject Classification 2010

Primary: 53A10

Secondary: 53C21, 53C42

Milestones

Received: 17 June 2019

Revised: 14 July 2020

Accepted: 1 November 2021

Published: 6 April 2022

Authors

Abigail Folha
Instituto de Matemática e Estatística Universidade Federal Fluminense Niterói Brazil

Harold Rosenberg
Instituto Nacional de Matemática Pura e Aplicada Rio de Janeiro Brazil

Vol. 316, No. 2, 2022

Abigail Folha and Harold Rosenberg

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors