Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity and convergence of 4-dimensional extremal Kahler metrics   We establish a regularity result for the metric on any 4-dimensional extremal
K\"ahler manifold, and a weak compactness theorem on the space of such metrics.
Specifically, the sectional curvature at a point is bounded when the quantity
$L^2(|\Riem|)$ in a surrounding ball is sufficiently small compared to the
pointwise norm of its scalar curvature. Consequently sequences of 4-dimensional
extremal K\"ahler metrics with uniformly bounded Calabi energies and scalar
curvature have convergent subsequences in the Gromov-Hausdorff topology.
Gromov-Hausdorff limits are length spaces with the structure of Riemannian
orbifolds away from finitely many point-like singularities of unknown
structure.

19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph