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PreprintCC BY 4.0HAL

Dirac eigenvalues and spacetime mean curvature estimates for DEC spin fill-ins

  • Simon Raulot
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Abstract

We establish spacetime counterparts of fill-in inequalities for spin initial data sets satisfying the dominant energy condition in dimensions three through seven, controlling the minimum and the integral of the norm of the spacetime mean curvature vector by intrinsic boundary data. The proof relies on a Reilly--MIT estimate for complete spin manifolds with compact boundary. As further consequences, under suitable nonnegativity assumptions, Gromov's hyperspherical-radius fill-in inequality and Bär's recent total mean-curvature estimate extend to complete, possibly noncompact spin manifolds with compact boundary.

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Cite

BibTeXRIS
BibTeX
@misc{raulot2026dirac,
  title = {{Dirac eigenvalues and spacetime mean curvature estimates for DEC spin fill-ins}},
  author = {Simon Raulot},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08720},
  eprint = {2609.08720},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05742588v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Dirac eigenvalues and spacetime mean curvature estimates for DEC spin fill-ins
AU  - Simon Raulot
PY  - 2026
DA  - 2026/09/08
PB  - HAL
DO  - 10.48550/arxiv.2609.08720
UR  - https://hal.science/hal-05742588v1
AB  - We establish spacetime counterparts of fill-in inequalities for spin initial data sets satisfying the dominant energy condition in dimensions three through seven, controlling the minimum and the integral of the norm of the spacetime mean curvature vector by intrinsic boundary data. The proof relies on a Reilly--MIT estimate for complete spin manifolds with compact boundary. As further consequences, under suitable nonnegativity assumptions, Gromov's hyperspherical-radius fill-in inequality and Bär's recent total mean-curvature estimate extend to complete, possibly noncompact spin manifolds with compact boundary.
ER  -