Intrinsic and extrinsic area density bounds are equivalent for complete connected smooth minimal immersions in Euclidean space of any dimension and codimension, enabling extension of Schoen-Simon-Yau estimates to n=6.
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A PDE-based improvement-of-flatness technique for annuli provides an alternative proof of the end-structure and asymptotics for finite Morse index minimal hypersurfaces with Euclidean area growth in low dimensions.
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Equivalence of intrinsic and extrinsic area bounds for minimal surfaces
Intrinsic and extrinsic area density bounds are equivalent for complete connected smooth minimal immersions in Euclidean space of any dimension and codimension, enabling extension of Schoen-Simon-Yau estimates to n=6.
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Improvement of flatness in annuli
A PDE-based improvement-of-flatness technique for annuli provides an alternative proof of the end-structure and asymptotics for finite Morse index minimal hypersurfaces with Euclidean area growth in low dimensions.