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arXiv · 2601.04027

Asymptotics of high-codimensional area-minimizing currents in hyperbolic space

Xumin Jiang·Jiongduo Xie
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Abstract

We investigate the asymptotic behavior of high-codimensional area-minimizing locally rectifiable currents in hyperbolic space, addressing a problem posed by F.H. Lin and establishing ``boundary regularity at infinity" results for such currents near their asymptotic boundaries under the standard Euclidean metric. Intrinsic obstructions to high-order regularity arise for odd-dimensional minimal surfaces, revealing a constraint dependent on the geometry of the asymptotic boundary. Our work advances the asymptotic theory of high-codimensional minimal surfaces in hyperbolic space.

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Xumin Jiang, Jiongduo Xie. 2026-01-07. Asymptotics of high-codimensional area-minimizing currents in hyperbolic space. https://arxiv.org/abs/2601.04027

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