PreprintCC BY 4.0arXiv
Gromov-Hausdorff instability of the positive mass theorem for Kähler manifolds
Abstract
We construct a sequence of AE Kähler metrics on ℂ2 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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BibTeX
@misc{merkel2026gromovhausdorff,
title = {{Gromov-Hausdorff instability of the positive mass theorem for Kähler manifolds}},
author = {Romy Marie Merkel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.32383},
eprint = {2609.32383},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32383},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gromov-Hausdorff instability of the positive mass theorem for Kähler manifolds
AU - Romy Marie Merkel
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2609.32383
UR - https://arxiv.org/abs/2609.32383
AB - 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.
ER -