Noncritical maps on geodesically complete spaces with curvature bounded above

Tadashi Fujioka

Published 2021-07-19Version 1

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 for distance maps on Alexandrov spaces with curvature bounded below.