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Positive Scalar Curvature on Foliations: Leafwise Band Width

  • Hengyu Chen
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Abstract

We establish an optimal leafwise width estimate for compact, spin, foliated bands with positive leafwise scalar curvature and infinite vertical Â-cowaist. This result addresses a special case of the foliated version of Gromov's band width conjecture and generalizes the scalar and mean curvature comparison theorem for spin bands due to Cecchini and Zeidler. Our approach, which also applies to spin foliations, relies on a local boundary value problem for deformed sub-Dirac operators on the Connes fibration. A key technical ingredient is a Lichnerowicz-type formula in the adiabatic limit for almost isometric foliations, which captures the sharp coefficient rank F/(rank F − 1) associated with the integrable subbundle F.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026positive,
  title = {{Positive Scalar Curvature on Foliations: Leafwise Band Width}},
  author = {Hengyu Chen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24786},
  eprint = {2609.24786},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24786},
}
RIS
TY  - UNPB
TI  - Positive Scalar Curvature on Foliations: Leafwise Band Width
AU  - Hengyu Chen
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24786
UR  - https://arxiv.org/abs/2609.24786
AB  - We establish an optimal leafwise width estimate for compact, spin, foliated bands with positive leafwise scalar curvature and infinite vertical Â-cowaist. This result addresses a special case of the foliated version of Gromov's band width conjecture and generalizes the scalar and mean curvature comparison theorem for spin bands due to Cecchini and Zeidler. Our approach, which also applies to spin foliations, relies on a local boundary value problem for deformed sub-Dirac operators on the Connes fibration. A key technical ingredient is a Lichnerowicz-type formula in the adiabatic limit for almost isometric foliations, which captures the sharp coefficient rank F/(rank F − 1) associated with the integrable subbundle F.
ER  -