This is an announcement for the paper “On asymptotically uniformly smoothness and nonlinear geometry of Banach spaces” by Bruno de Mendonça Bragahttps://arxiv.org/search/math?searchtype=author&query=de+Mendon%C3%A7a+Braga%2C+B.
Abstract: These notes concern the nonlinear geometry of Banach spaces, asymptotic uniform smoothness and several Banach-Saks-like properties. We study the existence of certain concentration inequalities in asymptotically uniformly smooth Banach spaces as well as weakly sequentially continuous coarse (Lipschitz) embeddings into those spaces. Some results concerning the descriptive set theoretical complexity of those properties are also obtained. We finish the paper with a list of open problem.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1808.03254