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arXiv · 2608.04364

Calabi-Yau Conjecture for Minimal Hypersurfaces in $\mathbb{R}^4$ with bounded geometry

Shrey Aryan·Alexander D. McWeeney·Giuseppe Tinaglia
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Abstract

The Calabi-Yau conjectures for complete minimal hypersurfaces $\Sigma^{n}\subset \mathbb{R}^{n+1}$ for $n\geq 2$ ask whether a complete minimal hypersurface must be unbounded, and more strongly whether it must be proper. In this work, we resolve this conjecture for complete, connected, embedded minimal hypersurfaces $ \Sigma^3 \subset \mathbb{R}^4$ with bounded second fundamental form and finite second Betti number $b_2(\Sigma;\mathbb{Z}_2)<\infty$.

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Shrey Aryan, Alexander D. McWeeney, Giuseppe Tinaglia. 2026-08-05. Calabi-Yau Conjecture for Minimal Hypersurfaces in $\mathbb{R}^4$ with bounded geometry. https://arxiv.org/abs/2608.04364

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