双曲三维流形的数量曲率与体积熵
微分几何
2025-06-06 v3 几何拓扑
摘要
我们证明任何闭双曲三维流形 M 都容许一个数量曲率至少为 -6、但体积熵严格大于 2 的黎曼度量。特别地，该构造给出了 I. Agol、P. Storm 和 W. Thurston 一个猜想的反例。
引用
@article{arxiv.2312.00138,
title = {Scalar curvature and volume entropy of hyperbolic 3-manifolds},
author = {Demetre Kazaras and Antoine Song and Kai Xu},
journal= {arXiv preprint arXiv:2312.00138},
year = {2025}
}
备注
v3 update: some details are added. 15 pages, 2 figures. Final version, accepted by JEMS