| Résume | We will discuss two results about the existence of closed minimal surfaces in
non-compact hyperbolic 3-manifolds.
In the first part, we will prove the following dichotomy: either all bounded
geometry surface groups admit a minimal surface, or there exists an example
with a minimal fibration.
In the second part we will discuss minimal surface existence for hyperbolic
handlebodies.
Based in joint work with Baris Coskunuzer, Zheng Huang and Ben Lowe.
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