Explicit constructions of universal R-trees and asymptotic geometry of hyperbolic spaces

Universal bounds for hyperbolic Dehn surgery

This paper gives a quantitative version of Thurston's hyperbolic Dehn surgery theorem. Applications include the first universal bounds on the number of non-hyperbolic Dehn fillings on a cusped hyperbolic 3-manifold, and estimates on the changes in volume and core geodesic length during hyperbolic Dehn filling. The proofs involve the construction of a family of hyperbolic cone-manifold structures, using infinitesimal harmonic deformations and analysis of geometric limits.

On the asymptotic geometry of the hyperbolic plane

Asymptotic subcone of an unbounded metric space is another metric space, capturing the structure of the original space at infinity. In this paper we define a functional metric space S which is an asymptotic subcone of the hyperbolic plane. This space is a real tree branching at every its point. Moreover, it is a homogeneous metric space such that any real tree with countably many vertices can be isometrically embedded into it. This implies that every such tree is also an asymptotic subcone of the hyperbolic plane.

通过边界刻画树与双曲空间

Characterising trees and hyperbolic spaces by their boundaries

本文用真 CAT(-1) 空间语言统一证明，粗局部紧树、各类双曲空间及八元数双曲平面均可由其视觉边界上的交比重构，融合了 Tits 与 Bourdon 的成果。

Properties of Caratheodory measure hyperbolic universal covers of compact Kahler manifolds

This article explores some properties of universal covers of compact Kahler manifolds, under the assumption of Caratheodory measure hyperbolicity. In particular, by comparing invariant volume forms, an inequality is established between the volume of canonical bundle of a compact Kahler manifolds and the Caratheodory measure of its universal cover (similar result as in [Kikuta 10]). Using similar method, an inequality is established between the restricted volume of canonical bundle of a compact Kahler manifolds and the restricted Caratheodory measure of its covering, solving a conjecture in [Ki…

通用覆盖上双曲球体积的一致比较

Uniform Comparison of Hyperbolic Ball Volumes on the Universal Cover

研究闭定向$n$ - 流形$M$上双曲度量相关问题，通过设定条件$\frac{\operatorname{Vol}_g(M)}{\|M\|_{\Delta}}<\delta_n$，得出满足此条件的黎曼度量$g$在通用覆盖上的双曲球体积相关结论。

Some Properties of Balanced Hyperbolic Compact Complex Manifolds

We prove several vanishing theorems for the cohomology of balanced hyperbolic manifolds that we introduced in our previous work and for the $L^2$ harmonic spaces on the universal cover of these manifolds. Other results include a Hard Lefschetz-type theorem for certain compact complex balanced manifolds and the non-existence of certain $L^1$ currents on the universal covering space of a balanced hyperbolic manifold.