A sufficient condition for a closed \((n-1)\)-dimensional surface to be homeomorphic to a sphere (Q1363302)

Some results obtained here establish sufficient conditions stated in terms of curvature, under which a surface (i.e., an \((n-1)\)-dimensional manifold embedded in \(\mathbb{R}^n\), \(n\geq 3)\) is homeomorphic to a sphere. The proofs apply the symmetrizations defined for convex surfaces in the author's papers [\textit{V. K. Ionin}, Sov. Math., Dokl. 4, 66-69 (1963; Zbl 0128.16405)] and [\textit{V. K. Ionin}, Sib. Mat. Zh. 6, 305-322 (1965; Zbl 0128.16501)].