Geometriae Dedicata

, Volume 195, Issue 1, pp 203–214 | Cite as

On a question of Gromov about the Wirtinger inequalities

  • Takefumi Kondo
  • Tetsu ToyodaEmail author
  • Takato Uehara
Original Paper


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).


CAT(0) space Wirtinger space \(\mathrm {Cycl}_k(0)\) space 

Mathematics Subject Classification (2010)

53C23 51F99 



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


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science, Faculty of ScienceKagoshima UniversityKagoshimaJapan
  2. 2.National Institute of Technology, Suzuka CollegeSuzukaJapan
  3. 3.Department of MathematicsSaga UniversitySaga-CityJapan

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