Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limits of manifolds with a Kato bound on the Ricci curvature   We study the structure of Gromov-Hausdorff limits of sequences of Riemannian
manifolds $\{(M_\alpha^n,g_\alpha)\}_{\alpha \in A}$ whose Ricci curvature
satisfies a uniform Kato bound. We first obtain Mosco convergence of the
Dirichlet energies to the Cheeger energy and show that tangent cones of such
limits satisfy the $\mathrm{RCD}(0,n)$ condition. When assuming a
non-collapsing assumption, we introduce a new family of monotone quantities,
which allows us to prove that tangent cones are also metric cones. We then show
the existence of a well-defined stratification in terms of splittings of
tangent cones. We finally prove volume convergence to the Hausdorff
$n$-measure.

30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs