We find a C ∞ one-parameter family of Riemannian metrics gt on R 3 for 0 ≤ t ≤ ε for some number ε with the following property: g 0 is the Euclidean metric on R 3 , the scalar curvatures of gt are strictly decreasing in t in the open unit ball and gt is isometric to the Euclidean metric in the complement of the ball.
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