Convex Bodies of Constant Width and Constant Brightness
Metric Geometry
2007-05-23 v1 Differential Geometry
Functional Analysis
Abstract
In 1926 S. Nakajima (= A. Matsumura) showed that any convex body in with constant width, constant brightness, and boundary of class 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.
Keywords
Cite
@article{arxiv.math/0306437,
title = {Convex Bodies of Constant Width and Constant Brightness},
author = {Ralph Howard},
journal= {arXiv preprint arXiv:math/0306437},
year = {2007}
}
Comments
20 pages