Characterizing $W^{2,p}$~submanifolds by $p$-integrability of global curvatures

Sławomir Kolasiński, Paweł Strzelecki, Heiko von der Mosel

We give sufficient and necessary geometric conditions, guaranteeing that an immersed compact closed manifold ${\Sigma }^m\subset {\mathbb{R}}^n$ of class $C^1$ and of arbitrary dimension and codimen…