Smooth Convex Bodies with Proportional Projection Functions
نویسنده
چکیده
For a convex body K ⊂ Rn and i ∈ {1, . . . , n− 1}, the function assigning to any i-dimensional subspace L of Rn, the i-dimensional volume of the orthogonal projection of K to L, is called the i-th projection function of K. Let K, K0 ⊂ Rn be smooth convex bodies of class C2 +, and let K0 be centrally symmetric. Excluding two exceptional cases, we prove that K and K0 are homothetic if they have two proportional projection functions. The special case when K0 is a Euclidean ball provides an extension of Nakajima’s classical three-dimensional characterization of spheres to higher dimensions.
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