Noncritical maps on geodesically complete spaces with curvature bounded above
Differential Geometry
2024-12-25 v5 Metric Geometry
Abstract
We define and study the regularity of distance maps on geodesically complete spaces with curvature bounded above. We prove that such a regular map is locally a Hurewicz fibration. This regularity can be regarded as a dual concept of Perelman's regularity in the geometry of Alexandrov spaces with curvature bounded below. As a corollary we obtain a sphere theorem for geodesically complete CAT(1) spaces.
Cite
@article{arxiv.2107.08859,
title = {Noncritical maps on geodesically complete spaces with curvature bounded above},
author = {Tadashi Fujioka},
journal= {arXiv preprint arXiv:2107.08859},
year = {2024}
}
Comments
Added proofs of Lemmas 3.1 and 3.2, Lemmas 5.3 and 5.4, and other minor changes