Roundness and metric type
The authors prove that if \(X\) is a Banach space including \(\ell_p^n\) uniformly in \(n\) and \(Y\) is metric space with metric type \(q>p\) then the inverse of each uniform homeomorphism from \(X\) to \(Y\) fails to satisfy any Lipschitz condition for large distances of order \(< q/p\). Some applications to cotype and roundness are discussed.
scientific article; zbMATH DE number 1563105
scientific article