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Convergence of isometries, with semicontinuity of symmetry of Alexandrov spaces


Author: John Harvey
Journal: Proc. Amer. Math. Soc. 144 (2016), 3507-3515
MSC (2010): Primary 53C23; Secondary 53C20
DOI: https://doi.org/10.1090/proc/12994
Published electronically: January 20, 2016
MathSciNet review: 3503718
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Abstract: The equivariant Gromov-Hausdorff convergence of metric spaces is studied. Where all isometry groups under consideration are compact Lie, it is shown that an upper bound on the dimension of the group guarantees that the convergence is by Lie homomorphisms. Additional lower bounds on curvature and volume strengthen this result to convergence by monomorphisms, so that symmetries can only increase on passing to the limit.


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Additional Information

John Harvey
Affiliation: Mathematisches Institut, Universität Münster, Einsteinstr. 62, 48149 Münster, Germany
Email: harveyj@uni-muenster.de

DOI: https://doi.org/10.1090/proc/12994
Received by editor(s): September 8, 2015
Published electronically: January 20, 2016
Additional Notes: The research was carried out within the Collaborative Research Center SFB 878, “Groups, Geometry and Actions”, supported by the Deutsche Forschungsgemeinschaft.
Communicated by: Lei Ni
Article copyright: © Copyright 2016 American Mathematical Society

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