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- W1814012308 abstract "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." @default.
- W1814012308 created "2016-06-24" @default.
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- W1814012308 date "2007-01-19" @default.
- W1814012308 modified "2023-09-27" @default.
- W1814012308 title "Observable concentration of mm-spaces into nonpositively curved manifolds" @default.
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