Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropies, volumes, and Einstein metrics   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.

37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat