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

A diameter gap for quotients of the unit sphere

  • Claudio Gorodski

    Universidade de São Paulo, Brazil

  • Christian Lange

    Ludwig-Maximilians-Universität München, Germany

  • Alexander Lytchak

    Karlsruhe Institute of Technology, Germany

  • Ricardo A. E. Mendes

    University of Oklahoma, Norman, USA
A diameter gap for quotients of the unit sphere cover
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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