2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125233Given a positive function F on Sn which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in Rn+1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas of Minkowski type for compact hypersurfaces in Rn+1. We give some new characterizations of the Wulff shape by use of our integral formulas of Minkowski type, in case F = 1 which reduces to some well-known results.10 pagesDifferential GeometryPrimary 53C42, 53A30; Secondary 53B25text