Smooth parameterizations of power-subanalytic sets and compositions of Gevrey functions

Abstract

We show that if $X$ is an $m$-dimensional definable set in ${\mathbb{R}}_{\text{an}}^{\text{pow}}$, the structure of real subanalytic sets with real power maps added, then for any positive integer r there exists a $C^r$-parameterization of X consisting of $c{r}^{m^3}$ maps for some constant $c$. Moreover, these maps are real analytic and this bound is uniform for a definable family.

Main result adjusted from r^{m^2} charts to r^{m^3} charts. Some extra results on mild functions have been added

Cited by in corpus (2)

• On a family of mild functions
• Mild parametrizations of power-subanalytic sets