Mathematische Zeitschrift

, Volume 277, Issue 1, pp 293–304

On the spread of positively curved Alexandrov spaces

Article

DOI: 10.1007/s00209-013-1255-5

Cite this article as:
Yokota, T. Math. Z. (2014) 277: 293. doi:10.1007/s00209-013-1255-5
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Abstract

It was proved by F. Wilhelm that Gromov’s filling radius of closed positively curved manifolds with a uniform lower bound on sectional curvature attains the maximum with the round sphere. Recently the author proved that this is also the case for closed finite-dimensional Alexandrov spaces with a positive lower curvature bound. These were proved as a corollary of a comparison theorem for the invariant called spread of those spaces. In this paper, we extend the latter result to infinite-dimensional Alexandrov spaces.

Keywords

Alexandrov spaceSpreadFilling radiusPacking radius

Mathematics Subject Classification (2000)

53C23

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyoto Japan
  2. 2.Mathematisches InstitutUniversity of MünsterMünsterGermany