Sufficiency of weighted jets using Paunescu’s singular metric

In this work we consider the Paunescu’s singular metric in the source to investigate the bi-Lipschitz and differential sufficiency in the set of weighted jets of map germs with a fixed weighted degree. This approach was motivated by the works of Paunescu, who investigated the V-sufficiency from the weighted point of view considering this metric in the source. Here we show a criterion for the bi-Lipschitz and differentiable sufficiency in the jet space of weighted jets taking into account the effect of this Paunescu’s singular metric on \(\mathbb {R}^n\) ${\mathbb{R}}^n$ .