Mathematische Zeitschrift

, Volume 277, Issue 1, pp 293-304

First online:

On the spread of positively curved Alexandrov spaces

  • Takumi YokotaAffiliated withResearch Institute for Mathematical Sciences, Kyoto UniversityMathematisches Institut, University of Münster Email author 

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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.


Alexandrov space Spread Filling radius Packing radius

Mathematics Subject Classification (2000)