Estimates of Gromov's box distance

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5 Citations (Scopus)


In 1999, M. Gromov introduced the box distance function □λ on the space of all mm-spaces. In this paper, by using the method of T. H. Colding, we estimate □λ(Sn,Sm) and □λ(ℂ Pn,ℂPm), where Sn is the n-dimensional unit sphere in ℝn +1 and ℂPn is the n-dimensional complex projective space equipped with the Fubini-Study metric. In particular, we give the complete answer to an exercise of Gromov's green book. We also estimate □λ (SO(n),SO(m)) from below, where SO(n) is the special orthogonal group.

Original languageEnglish
Pages (from-to)2911-2920
Number of pages10
JournalProceedings of the American Mathematical Society
Issue number8
Publication statusPublished - 2008 Aug


  • Box distance function
  • Mm-space
  • Observable distance function


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