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| Coarse Embedding into Uniformly ConvexBanach Spaces |
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Citation： |
Qinggang REN.Coarse Embedding into Uniformly ConvexBanach Spaces[J].Chinese Annals of Mathematics B,2014,35(5):733~742 |
| Page view： 1389
Net amount： 987 |
Authors： |
Qinggang REN; |
Foundation： |
the National Natural Science Foundation of China (No. 11301566) and the
Postdoc Scholarship (No. 2012M511900). |
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| Abstract： |
In this paper, the author studies the coarse embedding into uniformly convex Banach
spaces. The author proves that the property of coarse embedding into
Banach spaces can be preserved under taking the union of the metric
spaces under certain conditions. As an application, for a group $G$
strongly relatively hyperbolic to a subgroup $H$, the author proves
that $B(n)=\{g\in G\mid \abs{g}_{S\cup\mathscr{H}}\leq n\}$ admits a
coarse embedding into a uniformly convex Banach space if $H$ does. |
Keywords： |
Coarse embedding, Uniformly convex Banach spaces, Relative hyperbolic
groups |
Classification： |
46B20, 51F99 |
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