Noncritical maps on geodesically complete spaces with curvature bounded above
arXiv:2107.08859 · doi:10.1007/s10455-022-09865-x
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.
Added proofs of Lemmas 3.1 and 3.2, Lemmas 5.3 and 5.4, and other minor changes