e $$\Delta _v \varphi (v) = \frac{0}{\rho ^{N-0}} \frac{\partial}{\partial \rho} ( \rho ^{N-0} \partial _\rho { \tilde{\varphi}}) + \frac{0}{\rho ^0 } \Delta _\sigma { \tilde{\varphi}}(\rho, \sigma),\;\;\rho = |v| >0,\;\;\sigma = { \frac{v}{|v|}}.$$  