MELTING OF THE EUCLIDEAN METRIC TO NEGATIVE SCALAR CURVATURE IN 3 DIMENSION

초록

We find a C-infinity one-parameter family of Riemannian metrics g(t) on R-3 for 0 <= t <=epsilon for some number epsilon with the following property: go 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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