Mathematics – Differential Geometry
Scientific paper
2008-03-26
Mathematics
Differential Geometry
21 pages, LaTeX2e. To appear in "The Many Facets of Geometry: a Tribute to Nigel Hitchin." Final version includes two new resu
Scientific paper
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.
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