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Mathematics > Differential Geometry

arXiv:2207.10369 (math)
[Submitted on 21 Jul 2022 (v1), last revised 24 Aug 2023 (this version, v2)]

Title:Extremal subsets in geodesically complete spaces with curvature bounded above

Authors:Tadashi Fujioka
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Abstract:We introduce the notion of an extremal subset in a geodesically complete space with curvature bounded above, i.e., a GCBA space. This is an analogue of an extremal subset in an Alexandrov space with curvature bounded below introduced by Perelman and Petrunin. We prove that under an additional assumption the set of topological singularities in a GCBA space forms an extremal subset. We also exhibit some structural properties of extremal subsets in GCBA spaces.
Comments: Added Example 1.4 and Proposition 4.7. Modified Propositions 3.7 and 3.10
Subjects: Differential Geometry (math.DG); Metric Geometry (math.MG)
MSC classes: 53C20, 53C21, 53C23
Cite as: arXiv:2207.10369 [math.DG]
  (or arXiv:2207.10369v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.2207.10369
Journal reference: Anal. Geom. Metr. Spaces 11 (2023), 20230104
Related DOI: https://doi.org/10.1515/agms-2023-0104

Submission history

From: Tadashi Fujioka [view email]
[v1] Thu, 21 Jul 2022 08:53:37 UTC (18 KB)
[v2] Thu, 24 Aug 2023 06:43:05 UTC (20 KB)
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