2 problems

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The folklore conjecture on one-parameter families of asymptotic minimal surfaces
Let ${\mathbb S}^2_{\infty}=\partial_{\infty}\mathbb H^3$ be the sphere at infinity of hyperbolic $3$ -space, and let a Jordan curve be an embedded circle in…
Conjectureopenasymptotic-plateau-problem hyperbolic-geometry minimal-surfacesarXiv posted 3 days ago
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Conjecture on limits of area-minimizing surfaces with non-tall asymptotic boundary
Limit-boundary conjecture. The curve $\widehat{\Gamma}=\partial_\infty\Sigma$ is tall, and $\Gamma\mathbin{\triangle}\widehat{\Gamma}$ is a collection of nullhomotopic short curves…
Conjectureopenasymptotic-plateau-problem hyperbolic-geometry minimal-surfacesarXiv posted 3 days ago

The folklore conjecture on one-parameter families of asymptotic minimal surfaces