Abstract
Suppose that a sequence of Riemannian manifolds with Ricci curvature ≥ - k 2 converges to a Gromov-Hausdorff limit X . We show that if the amount of sectional curvature below K of the limiting manifolds approaches 0 in a suitable L 1 -sense, then X is an Alexandrov space of curvature ≥ K . As applications we present several generalizations of classical theorems.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
