Convex bodies of constant width and constant brightness

摘要

In 1926 Nakajima (=Matsumura) showed that any convex body in R-3 with constant width, constant brightness, and boundary of class C-2 is a ball. We show that the regularity assumption on the boundary is unnecessary, so that balls are the only convex bodies of constant width and brightness. (C) 2005 Elsevier Inc. All rights reserved.