Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Einstein-Maxwell Equations, Extremal Kahler Metrics, and
  Seiberg-Witten Theory   The Einstein-Maxwell equations on a smooth compact 4-manifold are
reformulated as a purely Riemannian variational problem analogous to Calabi's
variational problem for extremal Kahler metrics. Next, Seiberg-Witten theory is
used to show that these two problems are in fact intimately related. Extremal
Kahler metrics are then used to probe the limits of Seiberg-Witten curvature
estimates. The article then concludes with a brief survey of some recent
results on extremal Kahler metrics.

32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
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The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph