发表机构
Chern Institute of Mathematics & LPMC, Nankai University（南开大学陈省身数学研究所与理论物理中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明了正叶状数量曲率与无限垂直余腰条件下紧致自旋叶状带的最优叶状宽度估计，推广了Cecchini-Zeidler定理，并利用Connes纤维化上的子Dirac算子和绝热极限Lichnerowicz公式解决了Gromov带宽猜想的叶状特例。
AI 中文摘要
我们建立了紧致、自旋、叶状带在具有正叶状数量曲率和无限垂直$\widehat{A}$-余腰时的最优叶状宽度估计。该结果解决了Gromov带宽猜想叶状版本的一个特例，并推广了Cecchini和Zeidler关于自旋带的标量与平均曲率比较定理。我们的方法也适用于自旋叶状结构，依赖于Connes纤维化上变形子Dirac算子的局部边值问题。一个关键的技术要素是几乎等距叶状结构在绝热极限下的Lichnerowicz型公式，该公式捕捉了与可积子丛$F$相关的尖锐系数$\operatorname{rank} F/(\operatorname{rank} F - 1)$。
英文摘要
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 $F$.
Comments53 pages, 2 figures. Comments welcome!
