Una Relación entre las curvas medias de cuerpos convexos paralelos en espacios de curvatura constante

Abstract

Let Q be a closed convex hypersurface of class C3 of the n-dimensional space of constant curvature K=k. . Let Q (λ) be the hypersurfaces parallel to Q at distance λ . Let M (λ)denote the i-th mean curvature of Q (λ). We prove the identities where M ‘(λ ) = dMi (λ)/ dλ.From these identities wededuce some consequences for convex curves and surfaces (n = 2, 3); among them we get a proof of the inequality announced by Blaschke and first proved by Knothe by a very different way