Estimates of Gromov's box distance

Kei Funano

doi:10.1090/S0002-9939-08-09416-1

Estimates of Gromov's box distance

Kei Funano

INF - System Information Sciences

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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,S^m) and □λ(ℂ Pⁿ,ℂP^m), where Sⁿ is the n-dimensional unit sphere in ℝ^{n +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
Pages (from-to)	2911-2920
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	136
Issue number	8
DOIs	https://doi.org/10.1090/S0002-9939-08-09416-1
Publication status	Published - 2008 Aug 1

Keywords

Box distance function
Mm-space
Observable distance function

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-08-09416-1

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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.",

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T1 - Estimates of Gromov's box distance

AU - Funano, Kei

PY - 2008/8/1

Y1 - 2008/8/1

N2 - 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.

AB - 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.

KW - Box distance function

KW - Mm-space

KW - Observable distance function

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