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arXiv · 2609.32383

A tentacle example for the stability of the positive mass theorem for Kähler manifolds

Romy Marie Merkel
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Abstract

We construct a sequence of AE Kähler metrics on 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. This shows that, without any additional assumptions, the excision in Klemmensen's stability result for the positive mass theorem for Kähler manifolds is crucial, which aligns with the findings in the (3-dimensional) Riemannian case.

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Romy Marie Merkel. 2026-09-26. A tentacle example for the stability of the positive mass theorem for Kähler manifolds. https://arxiv.org/abs/2609.32383

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