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Einstein metrics with prescribed conformal infinity on the ball. (English) Zbl 0765.53034
The authors prove the existence of an Einstein metric on a Euclidean ball of any dimension, realizing, as its conformal infinity, any prescribed metric on the boundary sphere which is sufficiently close (in a suitable Hölder topology) to the standard metric.

MSC:
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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