SCALAR CURVATURE DECREASE FROM A HYPERBOLIC METRIC

초록

We find an explicit C^∞-continuous path of Riemannian metrics g_t on the 4-d hyperbolic space H4, for 0 ≤t ≤ε for some number ε > 0 with the following property: g0 is the hyperbolic metric on H^4, the scalar curvatures of g_t are strictly decreasing in t in an open ball and g_t is isometric to the hyperbolic metric in the complement of the ball.

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