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arXiv · 2605.18269

Bottom spectrum, vertical $\widehat{A}$-cowaist and scalar curvature rigidity

Daoqiang Liu
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Abstract

We introduce the vertical \(\widehat{A}\)-cowaist, a codimension-one invariant for partitioned manifolds. It extends the concept of infinite vertical \(\widehat{A}\)-cowaist for bands to arbitrary partitioned manifolds, which may be noncompact and have compact boundary. We establish a sharp inequality relating the scalar curvature, the bottom spectrum of the Laplacian, and this invariant. As an application, we obtain a high-dimensional analogue of Munteanu-Wang's bottom spectrum estimate. We also prove a quantitative strengthening of Anghel's theorem together with a boundary version, as well as a Calabi-Yau type theorem that goes beyond the dimensional restrictions of the earlier \(\mu\)-bubble method. Our approach is based on deformed Dirac operators.

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Daoqiang Liu. 2026-05-18. Bottom spectrum, vertical $\widehat{A}$-cowaist and scalar curvature rigidity. https://arxiv.org/abs/2605.18269

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