Observable concentration of mm-spaces into nonpositively curved manifolds
| dc.creator | Funano, Kei | |
| dc.date | 2007-01-19 | |
| dc.date | 2008-01-30 | |
| dc.date.accessioned | 2026-07-07T08:57:11Z | |
| dc.date.available | 2026-07-07T08:57:11Z | |
| dc.description | The measure concentration property of an mm-space $X$ is roughly described as that any 1-Lipschitz map on $X$ to a metric space $Y$ is almost close to a constant map. The target space $Y$ is called the screen. The case of $Y=\mathbb{R}$ is widely studied in many literature (see \cite{gromov}, \cite{ledoux}, \cite{mil2}, \cite{milsch}, \cite{sch}, \cite{tal}, \cite{tal2} and its reference). M. Gromov developed the theory of measure concentration in the case where the screen $Y$ is not necessarily $\mathbb{R}$ (cf. \cite{gromovcat}, {gromov2}, \cite{gromov}). In this paper, we consider the case where the screen $Y$ is a nonpositively curved manifolds. We also show that if the screen $Y$ is so big, then the mm-space $X$ does not concentrate. | |
| dc.description | 31 pages,1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0701535 | |
| dc.identifier | http://arxiv.org/abs/math/0701535 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146871 | |
| dc.subject | Metric Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C21, 53C23, 31C15 | |
| dc.title | Observable concentration of mm-spaces into nonpositively curved manifolds | |
| dc.type | text |