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arXiv · 2607.07986

Invariant solutions for the asymptotic Plateau problem in $\mathbb{H}^3$

Matheus Pimentel Gomes·Patrícia Kruse Klaser·Jaime Bruck Ripoll·Leonardo Prange Bonorino
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Abstract

In this paper, we present solutions to the asymptotic Plateau problem in the hyperbolic space $\mathbb{H}^3$. In this context, we exhibit solutions for curves that are invariant under the action of a one-parameter subgroup of isometries of $\mathbb{H}^3$. To achieve this, we prove the existence of foliations of $\mathbb{H}^3$ by minimal surfaces that are properly embedded, complete, and invariant under these subgroups, which are then used to solve the problem.

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Matheus Pimentel Gomes, Patrícia Kruse Klaser, Jaime Bruck Ripoll, Leonardo Prange Bonorino. 2026-07-08. Invariant solutions for the asymptotic Plateau problem in $\mathbb{H}^3$. https://arxiv.org/abs/2607.07986

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