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math.MG2013★ 2 cited
Characterization of ellipsoids as K-dense sets
Rolando Magnanini, Michele Marini
Let K\subset R^N be any convex body containing the origin. A measurable set G\subset R^N with finite and positive Lebesgue measure is said to be K-dense if, for any fixed r>0, the…
math.MG2012★ 4 cited
Characterization of ellipses as uniformly dense sets with respect to a family of convex bodies
Rolando Magnanini, Michele Marini
Let K \subset R^N be a convex body containing the origin. A measurable set G \subset R^N with positive Lebesgue measure is said to be uniformly K-dense if, for any fixed r > 0, the…