Asymptotic Invariants of Manifolds

研究了与最小体积熵有关的闭流形的几个渐近不变量，重点讨论了等周常数、最小特征值、球面体积和收缩常数。研究了这些不变量在同伦等价、同胚和同域条件下的性质。我们证明了这些不变量之间的不等式，并考虑了在自然出现渐近不变量的几何问题中的应用。

We investigate several asymptotic invariants of closed manifolds which are related to the minimal volume entropy, with special emphasis on the isoperimetric constant, the minimal eigenvalue, the spherical volume, and the systolic constant. We study the behaviour of these invariants under homotopy equivalence, under homeomorphism and under bordism. We prove inequalities between these invariants and we consider applications to geometric problems in which asymptotic invariants appear naturally.