On the smoothing problem (Q5949475)

The author proves that a topological manifold is smoothable whenever it possesses a Lipschitz atlas with Lipschitz size sufficiently close to 1. The smoothing problem in terms of Lipschitz atlases was also considered by \textit{Y. Shikata} [Osaka J. Math. 3, 293-301 (1966; Zbl 0168.44302)] and \textit{G. P. Weller} [ibid. 10, 507-510 (1973; Zbl 0276.57007)]. The author sharpens the results of these papers.