Smoothness of the metric of spaces with two-sided bounded Aleksandrov curvature (Q798961)

Let M be a space with two-sided bounded curvature in the sense of A. D. Aleksandrov. The author proves that the components \(g_{ij}\) of the metric tensor with respect to a certain coordinate system constructed by \textit{V. N. Berestovskij} [Sib. Mat. Zh. 16, 651-662 (1975; Zbl 0325.53059)] are locally Lipschitz and that in the neighborhood of any point of M one can introduce harmonic coordinates. Complete proofs of some results [Theorem 1,c) and Theorem 2] previously announced [Dokl. Akad. Nauk SSSR 250, 1056-1058 (1980; Zbl 0505.53015)] are also given. In particular, if \(\Omega\) is the domain of a system of harmonic coordinates, then with respect to such a system \(g_{ij}\) has second order differentials in the classical sense almost everywhere on \(\Omega\).