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On a question of Gromov about the Wirtinger inequalities

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Abstract

We prove that Gromov’s \(\mathrm {Cycl}_4(0)\) condition implies \(\mathrm {Wir}_k\) inequalities for any \(k \ge 4\), which answers a question of Gromov (J Math Sci N Y 119(2):178–200, 2004).

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Acknowledgements

The first author would like to thank Professor Hiroyasu Izeki for valuable discussions.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, Kagoshima University, 21-35 Korimoto 1-chome, Kagoshima, 890-0065, Japan

    Takefumi Kondo

  2. National Institute of Technology, Suzuka College, Shiroko-cho, Suzuka, Mie, 510-0294, Japan

    Tetsu Toyoda

  3. Department of Mathematics, Saga University, 1 Honjo-machi, Saga-City, Saga, 840-8502, Japan

    Takato Uehara

Authors
  1. Takefumi Kondo
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  2. Tetsu Toyoda
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  3. Takato Uehara
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Correspondence to Tetsu Toyoda.

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Kondo, T., Toyoda, T. & Uehara, T. On a question of Gromov about the Wirtinger inequalities. Geom Dedicata 195, 203–214 (2018). https://doi.org/10.1007/s10711-017-0284-3

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  • DOI: https://doi.org/10.1007/s10711-017-0284-3

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