On the Propagation of Singularities of Constant Curvature, Convex Hypersurfaces

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Article , Preprint 01 Jan 2025Embargo end date: 01 Oct 2024 English Publisher:Springer Nature Switzerland

Authors: Smith, Graham;

doi: 10.1007/978-3-032-00918-0_5 , 10.48550/arxiv.2410.09950

arXiv: 2410.09950

On the Propagation of Singularities of Constant Curvature, Convex Hypersurfaces

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Abstract

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

A brief review, by invitation, for a forthcoming volume in honour of Marcos Dajczer. 16 pages, 6 figures

Related Organizations

Pontifical Catholic University of Rio de Janeiro
Brazil

Keywords

Mathematics - Differential Geometry, 35J60, 52A20, 53C21, 53C42, 58K30, 58J47, 58J05, Differential Geometry (math.DG), FOS: Mathematics

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