Small volume of balls, large volume entropy and the Margulis constant
Small volume of balls, large volume entropy and the Margulis constant
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小球体积、大体积熵和 Margulis 常数
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发表时间：
2017
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通讯作者：
S. Sabourau
中科院分区：
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作者：
S. Sabourau
在他关于有界上同调的开创性工作中，Gromov证明了，在一定的拓扑条件下，每个小体积的闭黎曼流形都有大的体积熵。在本文中，我们使用另一种方法加强了这一结果的某些方面。更准确地说，我们证明了，在一些相似但不同的拓扑假设下，每个球体积小的闭黎曼流形都有大的体积熵。随着这一结果的证明，我们建立了一个新的涉及交换子收缩的收缩不等式和一个新的曲率自由估计，该估计将填充半径与Marguis常数联系起来。
In his seminal work about bounded cohomology, Gromov showed that, under some topological conditions, every closed Riemannian manifold of small volume has large volume entropy. In this article, we strengthen some aspects of this result using an alternative approach. More precisely, we prove that, under some similar, yet different, topological assumptions, every closed Riemannian manifold whose volume of balls is small has large volume entropy. Along the proof of this result, we establish a new systolic inequality involving the commutator systole and a new curvature-free estimate relating the filling radius to the Margulis constant.