Gromov-Hausdorff instability of the positive mass theorem for Kähler manifolds

Abstract

We construct a sequence of AE Kähler metrics on ${\mathbb{C}}^2$ with nonnegative and integrable scalar curvature whose ADM mass tends to zero but which, for a suitable choice of basepoints, fails to converge to Euclidean space in the pointed Gromov-Hausdorff sense.

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