Convergence of isometries, with semicontinuity of symmetry of Alexandrov spaces

Harvey, John ORCID: https://orcid.org/0000-0001-9211-0060 2016. Convergence of isometries, with semicontinuity of symmetry of Alexandrov spaces. Proceedings of the American Mathematical Society 144 (8) , pp. 3507-3515. 10.1090/proc/12994

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	American Mathematical Society
ISSN:	0002-9939
Last Modified:	10 Nov 2022 11:33
URI:	https://orca.cardiff.ac.uk/id/eprint/150995

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