Convex bodies of constant width and constant brightness |
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Authors: | Ralph Howard |
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Institution: | Department of Mathematics, University of South Carolina, Columbia, S.C. 29208, USA |
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Abstract: | In 1926 Nakajima (= Matsumura) showed that any convex body in R3 with constant width, constant brightness, and boundary of class C2 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. |
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Keywords: | primary 52A15 secondary 52A20 52A40 30C65 |
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