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Entropies, volumes, and Einstein metrics

D. Kotschick
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Abstract

We survey the definitions and some important properties of several asymptotic invariants of smooth manifolds, and discuss some open questions related to them. We prove that the (non-)vanishing of the minimal volume is a differentiable property, which is not invariant under homeomorphisms. We also formulate an obstruction to the existence of Einstein metrics on four-manifolds involving the volume entropy. This generalizes both the Gromov--Hitchin--Thorpe inequality and Sambusetti's obstruction.

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D. Kotschick. 2013-01-28. Entropies, volumes, and Einstein metrics. https://doi.org/10.1007/978-3-642-22842-1_2

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