标题： 负曲率流形的稀疏光谱刚性集 显示英文标题

标题： Sparse spectrally rigid sets for negatively curved manifolds

摘要： 假设$(M,\mathfrak{g})$是一个具有严格负截面曲率的紧致黎曼流形。 集合$E \subset \text{conj}(\pi_1(M))$中的共轭类被称为谱刚性的，如果当两个$M$上具有负曲率的黎曼度量$\mathfrak{g}_1, \mathfrak{g}_2$在$E$上具有相同的标记长度光谱时，则它们的标记长度光谱在处处一致。 在这项工作中，我们证明了存在任意稀疏的谱刚性集，并且从某种意义上说，它们存在于$\pi_1(M)$的每一个方向上。 显示英文摘要

摘要： Suppose that $(M,\mathfrak{g})$ is a compact Riemannian manifold with strictly negative sectional curvatures. A subset of conjugacy classes $E \subset \text{conj}(\pi_1(M))$ is called spectrally rigid if when two negatively curved Riemannian metrics $\mathfrak{g}_1, \mathfrak{g}_2$ on $M$ have the same marked length spectrum on $E$, then their marked length spectra coincide everywhere. In this work we show that there are arbitrarily sparse spectrally rigid sets and that they exist, in some sense, in every direction in $\pi_1(M)$.