Noncritical maps on geodesically complete spaces with curvature bounded above-Reference-Cited by-同舟云学术

Noncritical maps on geodesically complete spaces with curvature bounded above

Published:2022-07-31 Issue:3 Volume:62 Page:661-677
ISSN:0232-704X
Container-title:Annals of Global Analysis and Geometry
language:en
Short-container-title:Ann Glob Anal Geom

Author:

Fujioka Tadashi^ORCID

Abstract

AbstractWe 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.

Funder

Japan Society for the Promotion of Science

Publisher

Springer Science and Business Media LLC

Subject

Geometry and Topology,Analysis

Link

https://link.springer.com/content/pdf/10.1007/s10455-022-09865-x.pdf

Reference19 articles.

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2. translation in Russian Math. Surveys 47(2), 1-58 (1992)

3. Perelman, G.: Alexandrov’s spaces with curvatures bounded from below II, preprint, 1991

4. Perel'man, G.Ya.: Elements of Morse theory on Aleksandrov spaces. Algebra i Analiz 5(1), 232-241 (1993)

5. translation in St. Petersburg Math. J. 5(1), 205-213 (1994)

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