Absolute continuity for curvature measures of convex sets. III (Q696845)

The author continues his investigations of curvature measures and surface area measures of convex bodies which he started in [Math. Nachr. 195, 139-158 (1998; Zbl 0938.52003) and Math. Z. 232, 437-485 (1999; Zbl 0954.52006)]. In this third part, he proves two transfer principles by which the absolute continuity of the surface area measures of a convex body \(K\) (with or without bounded density) is related to the absolute continuity of the curvature measures (with or without bounded density) of the polar body \(K^*\). As applications he generalizes a result of the reviewer [Manuscr. Math. 8, 335-362 (1973; Zbl 0251.52007)] to curvature measures and he improves a stability theorem of Diskant.