On the spread of positively curved Alexandrov spaces Authors Takumi Yokota Research Institute for Mathematical Sciences Kyoto University Mathematisches Institut University of Münster Article

First Online: 04 December 2013 Received: 02 October 2012 Accepted: 29 October 2013 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
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 space
Spread
Filling radius
Packing radius
Partly supported by JSPS Postdoctoral Fellowships for Research Abroad.

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