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PreprintarXiv licencearXiv

Positive Scalar Curvature on Foliations: Long Neck Problem

  • Hengyu Chen
  • Guangxiang Su
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Abstract

We prove estimates for Gromov's Long Neck Foliated Conjecture in the spin cases, which involves leafwise scalar curvature. The same methods yield a quantitative version of a theorem of Su--Wang--Zhang and a Llarull-type theorem for closed foliated manifolds. A refinement, which involves mean curvature and partially generalizes a theorem of Cecchini--Zeidler, is also obtained.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026positive,
  title = {{Positive Scalar Curvature on Foliations: Long Neck Problem}},
  author = {Hengyu Chen and Guangxiang Su},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10344},
  eprint = {2610.10344},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10344},
}
RIS
TY  - UNPB
TI  - Positive Scalar Curvature on Foliations: Long Neck Problem
AU  - Hengyu Chen
AU  - Guangxiang Su
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10344
UR  - https://arxiv.org/abs/2610.10344
AB  - We prove estimates for Gromov's Long Neck Foliated Conjecture in the spin cases, which involves leafwise scalar curvature. The same methods yield a quantitative version of a theorem of Su--Wang--Zhang and a Llarull-type theorem for closed foliated manifolds. A refinement, which involves mean curvature and partially generalizes a theorem of Cecchini--Zeidler, is also obtained.
ER  -