Convex Bodies of Constant Width and Constant Brightness

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In 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 pages

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Metric Geometry, Differential Geometry, Functional Analysis, 52A15 (Primary) 52A20, 52A40, 30C62 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/67933

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0306437
 http://arxiv.org/abs/math/0306437

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arXiv