Entropies, volumes, and Einstein metrics

Details Entropies, volumes, and Einstein metrics Entropies, volumes, and Einstein metrics

2004-10-08

arxiv.org/abs/math/0410215v1

Mathematics

Differential Geometry

8 pages

Scientific paper

We give 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. We also prove that the (non-)vanishing
of the minimal volume is a differentiable property, which is not invariant
under homeomorphisms.

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