Observable concentration of mm-spaces into spaces with doubling measures
| dc.creator | Funano, Kei | |
| dc.date | 2007-01-19 | |
| dc.date.accessioned | 2026-07-07T07:41:56Z | |
| dc.date.available | 2026-07-07T07:41:56Z | |
| dc.description | The property of measure concentration is that an arbitrary 1-Lipschitz function $f:X\to \mathbb{R}$ on an mm-space $X$ is almost close to a constant function. In this paper, we prove that if such a concentration phenomenon arise, then any 1-Lipschitz map $f$ from $X$ to a space $Y$ with a doubling measure also concentrates to a constant map. As a corollary, we get any 1-Lipschitz map to a Riemannian manifold with a lower Ricci curvature bounds also concentrates to a constant map. | |
| dc.description | 8pages | |
| dc.identifier | https://arxiv.org/abs/math/0701534 | |
| dc.identifier | http://arxiv.org/abs/math/0701534 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122305 | |
| dc.subject | Metric Geometry | |
| dc.subject | 28E99;53C23 | |
| dc.title | Observable concentration of mm-spaces into spaces with doubling measures | |
| dc.type | text |