余紧负曲率流形的McKean刚性与\
McKean Rigidity for Cocompact Negatively Curved Manifolds and the \(p\)-Laplacian
AI总结：
该研究针对截面曲率不超过-1的闭黎曼流形，证明其万有覆叠的底部谱达到McKean下界当且仅当万有覆叠为常曲率-1的双曲空间，还推广了p-基本音的相关刚性结果，通过转化缺陷为平稳测度并利用热核正性完成证明。
AI中文摘要：
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英文摘要：
Let \((M^m,g)\) be a closed Riemannian manifold with \(\sec_g\leq-1\). We prove that the bottom spectrum of its universal cover attains McKean's lower bound if and only if the universal cover is hyperbolic space of constant sectional curvature \(-1\). More generally, for every \(1<p<\infty\), the variational \(p\)-fundamental tone satisfies \[ λ_{1,p}(\wti M) \geq\left(\frac{m-1}{p}\right)^p, \] and equality for some \(p\in(1,\infty)\) holds if and only if \(\wti M\cong\bH^m(-1)\). In that case, equality holds for every \(p\in(1,\infty)\). The proof converts the two McKean defects of a minimizing sequence into a stationary probability measure on the compact horospherical suspension; heat-kernel positivity then forces its zero-defect support to contain a complete leaf.
