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.
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