Convex Bodies of Constant Width and Constant Brightness
نویسنده
چکیده
Under the extra assumption that the boundary is of class C this was proven by S. Nakajima (= A. Matsumura) in 1926 Theorem 1 solves this problem. For convex bodies with C boundaries and positive curvature Nakajima’s result was generalized by Chakerian [?] in 1967 to “relative geometry” where the width and brightness are measured with with respect to some convex body K0 symmetric about the origin called the gauge body. While the main result of this paper is Theorem 1, Chakerian’s methods generalize and simplify parts of our original proof. The following isolates the properties required of the gauge body. Recall the Minkowski sum of two subsets A and B of R is A + B = {a + b : a ∈ A, b ∈ B}.
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