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Convergence of isometries, with semicontinuity of symmetry of Alexandrov spaces

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 نشر من قبل John Harvey
 تاريخ النشر 2015
  مجال البحث
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 تأليف John Harvey




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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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