A diameter gap for quotients of the unit sphere

Claudio Gorodski; Christian Lange; Alexander Lytchak; Ricardo A. E. Mendes

doi:10.4171/jems/1272

JournalsjemsVol. 25, No. 9pp. 3767–3793

A diameter gap for quotients of the unit sphere

Claudio Gorodski
Universidade de São Paulo, Brazil
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Christian Lange
Ludwig-Maximilians-Universität München, Germany
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Alexander Lytchak
Karlsruhe Institute of Technology, Germany
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Ricardo A. E. Mendes
University of Oklahoma, Norman, USA
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Abstract

We prove that for any isometric action of a group on a unit sphere of dimension larger than 1, the quotient space has diameter zero or larger than a universal dimension-independent positive constant.

Cite this article

Claudio Gorodski, Christian Lange, Alexander Lytchak, Ricardo A. E. Mendes, A diameter gap for quotients of the unit sphere. J. Eur. Math. Soc. 25 (2023), no. 9, pp. 3767–3793

DOI 10.4171/JEMS/1272