Property \((\beta)\) and uniform quotient maps

In 1999, Bates, Johnson, Lindenstrauss, Preiss and Schechtman asked whether a Banach space that is a uniform quotient of \(\ell_p\), \(1 < p \neq 2 < \infty\), must be isomorphic to a linear quotient of \(\ell_p\). We apply the geometric property \((\beta)\) of Rolewicz to the study of uniform and Lipschitz quotient maps, and answer the above question positively for the case \(1