Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An intrinsic flat limit of Riemannian manifolds with no geodesics   In this paper we produce a sequence of Riemannian manifolds $M_j^m$, $m \ge
2$, which converge in the intrinsic flat sense to the unit $m$-sphere with the
restricted Euclidean distance. This limit space has no geodesics achieving the
distances between points, exhibiting previously unknown behavior of intrinsic
flat limits. In contrast, any compact Gromov-Hausdorff limit of a sequence of
Riemannian manifolds is a geodesic space. Moreover, if $m\geq3$, the manifolds
$M_j^m$ may be chosen to have positive scalar curvature.

7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci