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Localized gluing of Riemannian metrics in interpolating their scalar curvature. (English) Zbl 1219.53041

Summary: We show that two smooth nearby Riemannian metrics can be glued interpolating their scalar curvature. The resulting smooth metric is the same as the starting ones outside the gluing region and has scalar curvature interpolating between the original ones. One can then glue metrics while maintaining inequalities satisfied by the scalar curvature. We also glue asymptotically Euclidean metrics to Schwarzschild ones and do the same for asymptotically Delaunay metrics, keeping bounds on the scalar curvature, if any. This extends the Corvino gluing near infinity to non-constant scalar curvature metrics.

MSC:

53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
35J60 Nonlinear elliptic equations
35J70 Degenerate elliptic equations
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