On ends of finite-volume noncompact manifolds of nonpositive curvature

• 成果类型: Article
• 署名作者: Ji, Ran; Wu, Yunhui
• 署名单位: Tsinghua University; Capital Normal University; Tsinghua University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01266-0
• 发表日期: 2024
• 页码: 735-777
• 关键词: CURVED SPACES; ISOMETRIES

摘要

In this paper we confirm a folklore conjecture which suggests that for a complete noncompact manifold M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M$\end{document} of finite volume with sectional curvature -1 <= K <= 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$-1 \leq K \leq 0$\end{document}, if the universal cover of M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M$\end{document} is a visibility manifold, then the fundamental group of each end of M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M$\end{document} is almost nilpotent.