Vol. 316, No. 2, 2022

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Entire constant mean curvature graphs in $\mathbb{H}^2\times\mathbb{R}$

Abigail Folha and Harold Rosenberg

Vol. 316 (2022), No. 2, 307–333
Abstract

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

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