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arXiv · 1905.06408

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

Siegfried Van Hille
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Abstract

We show that if $X$ is an $m$-dimensional definable set in $\mathbb{R}^\text{pow}_\text{an}$, 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 $cr^{m^3}$ maps for some constant $c$. Moreover, these maps are real analytic and this bound is uniform for a definable family.

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Siegfried Van Hille. 2019-05-15. Smooth parameterizations of power-subanalytic sets and compositions of Gevrey functions. https://doi.org/10.1017/s0013091521000298

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