This is an announcement for the paper “A new coarsely rigid class of Banach spaces” by Florent Baudierhttps://arxiv.org/search/math?searchtype=author&query=Baudier%2C+F, Gilles Lancienhttps://arxiv.org/search/math?searchtype=author&query=Lancien%2C+G, Pavlos Motakishttps://arxiv.org/search/math?searchtype=author&query=Motakis%2C+P, Thomas Schlumprechthttps://arxiv.org/search/math?searchtype=author&query=Schlumprecht%2C+T.
Abstract: We prove that the class of reflexive asymptotic-$c_0$ Banach spaces is coarsely rigid, meaning that if a Banach space $X$ coarsely embeds into a reflexive asymptotic-$c_0$ space $Y$, then $X$ is also reflexive and asymptotic-$c_0$. In order to achieve this result we provide a purely metric characterization of this class of Banach spaces which is rigid under coarse embeddings. This metric characterization takes the form of a concentration inequality for Lipschitz maps on the Hamming graphs.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1806.00702