Geometry and Rank of Fibered Hyperbolic 3-Manifolds

On the Growth of hyperbolic geodesics in rank 1 manifolds

We give a formula for the topological pressure of the geodesic flow of a compact rank 1 manifold in terms of the growth of the number of closed hyperbolic (rank 1) geodesics. We derive an equidistribution result for these geodesics with respect to equilibrium states. This generalize partially a result of G. Knieper \cite{kni} to non constant potentiels.

一种组合高阶双曲性条件

A combinatorial higher-rank hyperbolicity condition

本研究提出组合高阶双曲性即(n,δ)-双曲性的概念，证明其基础性质，并验证Helly群与分层双曲群可在对应空间上几何作用，拓展了双曲性理论。

极小双曲多项式与齐次锥的秩

Minimal hyperbolic polynomials and ranks of homogeneous cones

本文围绕弦稀疏模式对应锥的对偶的极小双曲多项式计算展开，探究齐次锥秩与极小多项式的关联，否定了过往论文的一个问题，并给出非秩一生成（ROG）双曲性锥的齐次锥实例。