Extremal subsets in geodesically complete spaces with curvature bounded above
Differential Geometry
2024-12-25 v2 Metric Geometry
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.
Keywords
Cite
@article{arxiv.2207.10369,
title = {Extremal subsets in geodesically complete spaces with curvature bounded above},
author = {Tadashi Fujioka},
journal= {arXiv preprint arXiv:2207.10369},
year = {2024}
}
Comments
Added Example 1.4 and Proposition 4.7. Modified Propositions 3.7 and 3.10