preprint

Inserted: 11 may 2026

Year: 2026

Abstract:

We show that intrinsic and extrinsic area density bounds are equivalent, with matching asymptotic values, for complete, connected, smooth minimal immersions $i:Σ^d\to\mathbb{R}^N$ of any dimension and codimension. Combining our results with a recent breakthrough by Bellettini, we extend the Schoen--Simon--Yau curvature estimates for smoothly immersed, two-sided, stable minimal hypersurfaces $i:Σ^n\to\mathbb{R}^{n+1}$ with bounded intrinsic area density to the missing case $n=6$, which had remained open since.