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arXiv · 2609.24786

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 $\widehat{A}$-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 $\operatorname{rank} F/(\operatorname{rank} F - 1)$ associated with the integrable subbundle $F$.

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Hengyu Chen. 2026-09-21. Positive Scalar Curvature on Foliations: Leafwise Band Width. https://arxiv.org/abs/2609.24786

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