共形流与负曲率三维流形的熵
Conformal currents and the entropy of negatively curved three-manifolds
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中文总结 AI 辅助
该研究通过刻画闭双曲三维流形上测地流与共形流的交集，得到负曲率度量相关熵与面积比的精确界，并给出三维莫斯托刚性定理的新证明。
中文摘要 AI 辅助
本文刻画了闭双曲三维流形上测地流与共形流的交集。我们借此证明了若干涉及负曲率度量的Liouville熵、极小曲面熵与面积比的精确界。利用这些思路，我们还给出了三维情形下Mostow Rigidity Theorem（莫斯托刚性定理）的一种新证明。
英文摘要
In this paper, we describe the intersection between geodesic and conformal currents on closed hyperbolic three-manifolds. We use this to prove some sharp bounds which involve the Liouville entropy of a negatively curved metric, the minimal surface entropy, and the area ratio. Using these ideas we also give a new proof of the Mostow Rigidity Theorem in the three-dimensional case.
