3 papers
math.FA2025
Asymptotic and nonlinear geometries of Banach spaces and their interactions
Florent P. Baudier, Gilles Lancien
This book discusses the interactions between the (nonlinear) metric structure of Banach spaces and their linear asymptotic behavior. The overarching problem is to understand how th…
math.MG2025
Umbel convexity and the geometry of trees
Florent P. Baudier, Chris Gartland
For every , a new metric invariant called umbel -convexity is introduced. The asymptotic notion of umbel convexity captures the geometry of countably branching t…
math.FA2024
On asymptotic B-convexity and infratype
Florent Baudier, Audrey Fovelle
In this note, we introduce and study the notions of asymptotic B-convexity and asymptotic infratype , and we prove asymptotic analogs of a series of results due to Giesy \cite{G…