Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of eigenvalues and observable diameter in RCD$(1,\infty)$
  spaces   We study stability of the spectral gap and observable diameter for
metricmeasure spaces satisfying the RCD(1, $\infty$) condition. We show that if
such a space has an almost maximal spectral gap, then it almost contains a
Gaussian component, and the Laplacian has eigenvalues that are close to any
integers, with dimension-free quantitative bounds. Under the additional
assumption that the space admits a needle disintegration, we show that the
spectral gap is almost maximal iff the observable diameter is almost maximal,
again with quantitative dimension-free bounds.

13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg