On two conjectures of franz hering about convex surfaces

Abstract

In this paper we show that from the point of view of the Baire categories for most convex bodies no shadow boundary is included in a hyperplane. A related, more quantitative question is also considered. It receives in general a negative answer and in the C2-case a positive one, but remains open in the C1-case. © 1991 Springer-Verlag New York Inc.