标题： 截去双曲流形中完全测地边界组件 显示英文标题

标题： Coning off totally geodesic boundary components of a hyperbolic manifold

摘要： 设 M 是一个具有全测地边界的紧双曲流形。 如果边界的有效可入半径大于边界的法向有效可入半径的某一显式函数，我们证明可以在通过将 M 的每个边界组件锥化为一点所得到的空间上赋予一个负曲率度量。 此外，我们给出了局部凸子集在锥化下保持局部凸性的明确几何条件。 群论上，我们得出锥化空间的基本群是双曲的，并且锥化局部凸子集的基本群的像是一个拟凸子群。 显示英文摘要

摘要： Let M be a compact hyperbolic manifold with totally geodesic boundary. If the injectivity radius of the boundary is larger than an explicit function of the normal injectivity radius of the boundary, we show that there is a negatively curved metric on the space obtained by coning each boundary component of M to a point. Moreover, we give explicit geometric conditions under which a locally convex subset of M gives rise to a locally convex subset of the cone-off. Group-theoretically, we conclude that the fundamental group of the cone-off is hyperbolic and the image of the fundamental group of the coned-off locally convex subset is a quasi-convex subgroup.