Abstract
I show that if a geodesic space has curvature bounded below locally in the sense of Alexandrov then its completion has the same lower curvature bound globally.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alexander, S., Bishop, R.: The Hadamard–Cartan theorem in locally convex spaces. l’Enseignement Math. 36, 309–320 (1990)
Alexander, S., Bishop, R.: Warped products admitting a curvature bound. arXiv:1509.00380 [math.DG]
Alexander, S., Kapovitch, V., Petrunin, A.: Alexandrov geometry. www.math.psu.edu/petrunin
Burago, Y., Gromov, M., Perelman, G.: A.D. Aleksandrov spaces with curvatures bounded below. Russ. Math. Surv. 47(2), 1–58 (1992)
Petrunin, A.: Parallel transportation for Alexandrov space with curvature bounded below. Geom. Funct. Anal. 8(1), 123–148 (1998)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Petrunin, A. A globalization for non-complete but geodesic spaces. Math. Ann. 366, 387–393 (2016). https://doi.org/10.1007/s00208-015-1295-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00208-015-1295-8