Convex Bodies of Constant Width and Constant Brightness

2003/06/30 by Ralph Howard, Howard, Ralph
Computer Science · Engineering · Materials Science · Mathematics · #30C62 (Secondary) #52A15 (Primary) 52A20 #52A40 #Advanced Graph Theory Research #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Quasicrystal Structures and Properties #graph theory and CDMA systems #math.DG #math.FA #math.MG #msc:30C62 #msc:52A15 #msc:52A20 #msc:52A40

paper · pdf · doi:10.48550/arxiv.math/0306437

20 pages

arxiv created 2003/06/30 · openalex publication_date 2003/06/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1926 S. Nakajima (= A. 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.

Citations

• On the solutions of quasi-linear elliptic partial differential equations

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