Estimates of Gromov's box distance

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dc.creatorFunano, Kei
dc.date2007-06-21
dc.date.accessioned2026-07-07T08:11:31Z
dc.date.available2026-07-07T08:11:31Z
dc.descriptionIn 1999, M. Gromov introduced the box distance function $\sikaku$ on the space of all mm-spaces. In this paper, by using the method of T. H. Colding (cf. \cite[Lemma 5.10]{Colding}), we estimate $\sikaku(\mathbb{S}^n,\mathbb{S}^m)$ and $\sikaku (\mathbb{C}P^n, \mathbb{C}P^m)$, where $\mathbb{S}^n$ is the $n$-dimensional unit sphere in $\mathbb{R}^{n+1}$ and $\mathbb{C}P^n$ is the $n$-dimensional complex projective space equipped with the Fubini-Study metric. In paticular, we give the complete answer to an Exercise of Gromov's Green book (cf. \cite[Section $3{1/2}.18$]{gromov}). We also estimate $\sikaku \big(SO(n), SO(m)\big)$ from below, where SO(n) is the special orthogonal group.
dc.description11pages
dc.identifierhttps://arxiv.org/abs/0706.3086
dc.identifierhttp://arxiv.org/abs/0706.3086
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132142
dc.subjectMetric Geometry
dc.subject28E99, 53C23
dc.titleEstimates of Gromov's box distance
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