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We describe the structure of the singular sets of constant curvature, convex hypersurfaces in hyperbolic space for general convex curvature functions. We apply this structure theorem to the study of the ideal Plateau problem in hyperbolic space for such curvature functions.

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On the Propagation of Singularities of Constant Curvature, Convex Hypersurfaces

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  • 发表日期：

    2025年

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  • Graham Andrew Smith

摘要

We describe the structure of the singular sets of constant curvature, convex hypersurfaces in hyperbolic space for general convex curvature functions. We apply this structure theorem to the study of the ideal Plateau problem in hyperbolic space for such curvature functions.