Observable concentration of mm-spaces into nonpositively curved manifolds

Details Observable concentration of mm-spaces into nonpositively curved manifolds Observable concentration of mm-spaces into nonpositively curved manifolds

2007-01-19

arxiv.org/abs/math/0701535v12

Mathematics

Metric Geometry

31 pages,1 figure

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Observable concentration of mm-spaces into nonpositively curved manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Observable concentration of mm-spaces into nonpositively curved manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Observable concentration of mm-spaces into nonpositively curved manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-70865