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PreprintarXiv licencearXiv

Strict Stability of the ADM Mass and Static Vacuum Extensions

  • Zhongshan An
  • Lan-Hsuan Huang
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Abstract

We introduce a notion of strict stability for the ADM mass on asymptotically flat manifolds with boundary and establish several of its fundamental properties. In particular, we show that a strictly stable static vacuum metric is a strict local ADM mass minimizer, thus proving a local version of Bartnik's Mass Minimizer Conjecture near Euclidean exterior regions. Our approach also gives a new proof of the existence of static vacuum extensions for nearby Bartnik boundary data on arbitrary exterior regions of Euclidean space.

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Cite

BibTeXRIS
BibTeX
@misc{an2026strict,
  title = {{Strict Stability of the ADM Mass and Static Vacuum Extensions}},
  author = {Zhongshan An and Lan-Hsuan Huang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28101},
  eprint = {2609.28101},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28101},
}
RIS
TY  - UNPB
TI  - Strict Stability of the ADM Mass and Static Vacuum Extensions
AU  - Zhongshan An
AU  - Lan-Hsuan Huang
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28101
UR  - https://arxiv.org/abs/2609.28101
AB  - We introduce a notion of strict stability for the ADM mass on asymptotically flat manifolds with boundary and establish several of its fundamental properties. In particular, we show that a strictly stable static vacuum metric is a strict local ADM mass minimizer, thus proving a local version of Bartnik's Mass Minimizer Conjecture near Euclidean exterior regions. Our approach also gives a new proof of the existence of static vacuum extensions for nearby Bartnik boundary data on arbitrary exterior regions of Euclidean space.
ER  -