Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local cut points and metric measure spaces with Ricci curvature bounded
  below   A local cut point is by definition a point that disconnectes its sufficiently
small neighborhood. We show that there exists an upper bound for the degree of
a local cut point in a metric measure space satisfying the generalized
Bishop--Gromov inequality. As a corollary, we obtain an upper bound for the
number of ends of such a space. We also obtain some obstruction conditions for
the existence of a local cut point in a metric measure space satisfying the
Bishop--Gromov inequality or the Poincar\'{e} inequality. For example, the
measured Gromov--Hausdorff limits of Riemannian manifolds with a lower Ricci
curvature bound satisfy these two inequalities.

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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat