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Published in last 50 years
A characterization of spheres in Euclidean space
A characterization of spheres among compact 3-bodies satisfying Crofton's theorem
Brick partitionings are used repeatedly to prove, by definition, the classical Kline $2$-sphere characterization.
A characterization of spheres among convex 3-bodies
A sphere characterization related to Blaschke’s conjecture
The Kline sphere characterization problem