Convex Bodies of Constant Width and Constant Brightness

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67933In 1926 S. Nakajima (= A. 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.20 pagesMetric GeometryDifferential GeometryFunctional Analysis52A15 (Primary) 52A20, 52A40, 30C62 (Secondary)Convex Bodies of Constant Width and Constant Brightnesstext