Embedding proper ultrametric spaces into $\ell_p$ and its application to   nonlinear Dvoretzky's theorem
  We prove that every proper ultrametric space isometrically embeds into $\ell_p$ for any $p\geq 1$. As an application we discuss an $\ell_p$-version of nonlinear Dvoretzky's theorem. 
Kei Funano
math.MG