随机测地线典范提升补的体积界
几何拓扑
2022-03-01 v2
摘要
给定闭双曲曲面中一条填充本原测地线曲线，人们可通过该曲线到射影切丛的典范提升的补获得一个双曲三维流形。本文给出了这类流形体积相对于一般曲线长度的首个已知下界。我们表明，从下方估计体积可归约为单位切丛中的计数问题，并应用测地流的指数多重混合结果予以解决。
引用
@article{arxiv.2108.08419,
title = {Volume bounds for the canonical lift complement of a random geodesic},
author = {Tommaso Cremaschi and Yannick Krifka and Dídac Martínez-Granado and Franco Vargas Pallete},
journal= {arXiv preprint arXiv:2108.08419},
year = {2022}
}
备注
55 pages, 6 figures. Added a new result on asymptotic density of closed geodesics. Section 4 updated with asymptotic density background, and lemma relating it to original random geodesic model. Section 5 simplified to use only dynamical arguments. Section 7 updated