论文标题
短时代的近似对标记长度光谱的控制
Approximate control of the marked length spectrum by short geodesics
论文作者
论文摘要
已知封闭式弯曲的歧管$（M，G）$的明显长度光谱（MLS）在各种情况下确定度量$ G $。我们表明，在这些情况下，MLS在足够大的有限集上的（大约）值大致确定度量。我们的方法是在Arxiv中恢复我们主要定理的假设：2203.12128，即MLS功能在整个$ M $的封闭地理器中的乘法紧密性。我们主要使用动态工具和参数，但要格外小心地显示所涉及的常数仅取决于有关给定的Riemannian指标的具体几何信息，例如维度，截面曲率界限和注射性radii。
The marked length spectrum (MLS) of a closed negatively curved manifold $(M, g)$ is known to determine the metric $g$ under various circumstances. We show that in these cases, (approximate) values of the MLS on a sufficiently large finite set approximately determine the metric. Our approach is to recover the hypotheses of our main theorems in arXiv:2203.12128, namely multiplicative closeness of the MLS functions on the entire set of closed geodesics of $M$. We use mainly dynamical tools and arguments, but take great care to show the constants involved depend only on concrete geometric information about the given Riemannian metrics, such as the dimension, sectional curvature bounds, and injectivity radii.
