# On the existence of foliations by solutions to the exterior Dirichlet problem for the minimal surface equation

@inproceedings{Aiolfi2021OnTE,
title={On the existence of foliations by solutions to the exterior Dirichlet problem for the minimal surface equation},
author={Ari J. Aiolfi and Daniel Bustos and Jaime Ripoll},
year={2021}
}
• Published 27 December 2020
• Mathematics
Given an exterior domain Ω of C class of R, n ≥ 3, it is proved the existence of a foliation of the closure of an open set of Rn+1\ (∂Ω× R) which leaves are graphs of the solutions of the exterior Dirichlet problem on Ω for the minimal surface equation containing the trivial solution. The leaves have horizontal ends and are parametrized by the maximum angle α ∈ [0, π/2] that the Gauss map in R of the leaves make with the vertical direction at the boundary of the domain. The solutions have a…
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