2 problems

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Properness and cubic area growth conjecture for finite-genus constant mean curvature surfaces
Let $N$ be a complete flat $3$ -manifold, and let $M$ be a complete connected $H$ -surface embedded in $N$ with finite genus. Let $W$ denote its closed mean-convex complement when…
Conjectureopenarea-growth constant-mean-curvature-surfaces proper-embedded-surfacesarXiv posted 2 days ago
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Nonexistence of quadratic-area-growth entire minimal graphs in Nil $_3$
Let Nil $_3$ denote the Heisenberg space, and call a surface an entire minimal graph if it is a minimal graph over the whole horizontal base. A surface has quadratic area growth if…
Conjectureopenarea-growth minimal-surfaces nil-geometryarXiv posted 2 days ago

Properness and cubic area growth conjecture for finite-genus constant mean curvature surfaces