Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the smallest Laplace eigenvalue for naturally reductive metrics on
  compact simple Lie groups   Eldredge, Gordina and Saloff-Coste recently conjectured that, for a given
compact connected Lie group $G$, there is a positive real number $C$ such that
$\lambda_1(G,g)\operatorname{diam}(G,g)^2\leq C$ for all left-invariant metrics
$g$ on $G$. In this short note, we establish the conjecture for the small
subclass of naturally reductive left-invariant metrics on a compact simple Lie
group.

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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an