二维紧集上的持久丛

Unique ergodicity of the horocycle flow of a higher genus compact surface with no conjugate points and continuous Green bundles

We show that the horocyclic flow of an orientable compact higher genus surface without conjugate points and with continuous Green bundles is uniquely ergodic. The result applies to nonflat nonpositively curved surfaces and generalizes a classical result of Furstenberg and Marcus in negative curvature. The proof relies on the definition of a uniformly expanding parametrization on the quotient by the strips of the surface.

Topologically stable and $β$-persistent points of group actions

In this paper, we introduce topologically stable points, $β$-persistent points, $β$-persistent property, $β$-persistent measures and almost $β$-persistent measures for first countable Hausdorff group actions of compact metric spaces. We prove that the set of all $β$-persistent points is measurable and it is closed if the action is equicontinuous. We also prove that the set of all $β$-persistent measures is a convex set and every almost $β$-persistent measure is a $β$-persistent measure. Finally, we prove that every equicontinuous pointwise topologically stable first countable Hausdorff group a…

Geodesic flows modeled by expansive flows: Compact surfaces without conjugate points and continuous Green bundles

We study the geodesic flow of a compact surface without conjugate points and genus greater than one and continuous Green bundles. Identifying each strip of bi-asymptotic geodesics induces an equivalence relation on the unit tangent bundle. Its quotient space is shown to carry the structure of a 3-dimensional compact manifold. This manifold carries a canonically defined continuous flow which is expansive, time-preserving semi-conjugate to the geodesic flow, and has a local product structure. An essential step towards the proof of these properties is to study regularity properties of the horosph…

具有半正反典范丛的紧致Kähler曲面

Compact Kähler surfaces with semipositive anticanonical bundle

本文分类了具有半正反典范丛的紧致Kähler曲面，并解决了Demailly-Peternell-Schneider关于光滑三次曲线上9点爆破的问题。

紧群丛的 Peter-Weyl 定理与相对遍历紧扩张的几何表示

A Peter-Weyl theorem for compact group bundles and the geometric representation of relatively ergodic compact extensions

本文证明相对遍历保测扩张具有相对离散谱等价于可由紧齐性空间丛作斜积表示，并通过拓扑动力学分类及紧群丛的 Peter-Weyl 型定理完成推广。

余切丛的慢熵与辛同构

Slow entropy and symplectomorphisms of cotangent bundles

我们考虑一个度量映射迭代下子流形的多项式体积增长的熵型不变量，并对紧基上余切丛的以下几类辛同胚建立了这个不变量的一致下界：1）与单位元辛同位素的非全同紧支撑辛同胚，2）由经典Hamilton函数生成的辛同胚，3）紧秩1对称空间上的Dehn扭似辛同胚。