Abstract
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 language | English |
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Pages (from-to) | 2911-2920 |
Number of pages | 10 |
Journal | Proceedings of the American Mathematical Society |
Volume | 136 |
Issue number | 8 |
DOIs | |
Publication status | Published - 2008 Aug 1 |
Externally published | Yes |
Keywords
- Box distance function
- Mm-space
- Observable distance function
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics