For closed surfaces of genus at least two, the Gauss equation for minimal immersions into hyperbolic 3-manifolds admits solutions exactly for t in [0, τ0], with a unique stable solution and a family of unstable solutions that blow up as t→0, with genus-dependent limits.
M onge- A mp\`ere equations , Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol
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Bifurcation for Minimal Surface Equation in Hyperbolic $3$-Manifolds
For closed surfaces of genus at least two, the Gauss equation for minimal immersions into hyperbolic 3-manifolds admits solutions exactly for t in [0, τ0], with a unique stable solution and a family of unstable solutions that blow up as t→0, with genus-dependent limits.