On the preparation theorem for subanalytic functions (Q2754590)

The author presents an introduction to the preparation theorem for subanalytic functions. This interesting theorem originated in his earlier works on Lipschitz stratifications of subanalytic sets and found many applications as a strong tool to study various properties of singular spaces such as for instance: integration on subanalytic sets, o-minimality, order of contact between solutions of differential equations and cell decomposition of subexponential sets. NEWLINENEWLINENEWLINEThe paper is very well written and shows many relations with earlier classical concepts like Puisseux Theorem, Jung-Abhyankar Theorem and rectilinearization. NEWLINENEWLINENEWLINEIn the second part integration with parameter on subanalytic sets is discussed and its relation with bi-lipschitz invariants is also considered. NEWLINENEWLINENEWLINEThe last section explains the Lipschitz structure of subanalytic sets.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00034].