The minimal entropy problem for 3-manifolds with zero simplicial volume

积分叶状单纯体积与遍历分解

Integral foliated simplicial volume and ergodic decomposition

本文建立了积分叶状单纯体积沿遍历分解的积分公式，类比于群的代价的遍历分解公式，为几何拓扑与动力系统交叉领域提供了新工具。

Amenable covers and integral foliated simplicial volume

In analogy with ordinary simplicial volume, we show that integral foliated simplicial volume of oriented closed connected aspherical $n$-manifolds that admit an open amenable cover of multiplicity at most $n$ is zero. This implies that the fundamental groups of such manifolds have fixed price and are cheap as well as reproves some statements about homology growth.

关于环面映射环的循环覆盖的积分单纯体积

On the integral simplicial volume of cyclic covers of mapping tori

本文研究了环面映射环的循环覆盖的积分单纯体积的渐近行为，通过积分填充体积建立了极限的上下界，并揭示了其与拓扑熵的联系及若干新应用。

通过叶状单纯形与对偶性研究单纯体积

Simplicial volume via foliated simplices and duality

该研究在带基本群保测作用的闭流形框架下，通过定义奇异叶状同调与有界上同调，证明叶状基本类范数等于流形单纯体积，并建立非球面情形下的等距同构与零化准则，形式化了Gromov的相关思路。

Entropy rigidity for finite volume strictly convex projective manifolds

We prove entropy rigidity for finite volume strictly convex projective manifolds in dimensions $\geq 3$, generalizing the work of arXiv:1708.03983 to the finite volume setting. The rigidity theorem uses the techniques of Besson, Courtois, and Gallot's entropy rigidity theorem. It implies uniform lower bounds on the volume of any finite volume strictly convex projective manifold in dimensions $\geq 3$.

Entropy Rigidity and Hilbert Volume

For a closed, strictly convex projective manifold of dimension $n\geq 3$ that admits a hyperbolic structure, we show that the ratio of Hilbert volume to hyperbolic volume is bounded below by a constant that depends only on dimension. We also show that for such spaces, if topological entropy of the geodesic flow goes to zero, the volume must go to infinity. These results follow from adapting Besson--Courtois--Gallot's entropy rigidity result to Hilbert geometries.