Abstract
We prove a simple, explicit formula for the mass of any asymptotically locally Euclidean (ALE) Kahler manifold, assuming only the sort of weak fall-off conditions required for the mass to actually be well-defined. For ALE scalar-flat Kahler manifolds, the mass turns out to be a topological invariant, depending only on the underlying smooth manifold, the first Chern class of the complex structure, and the Kahler class of the metric. When the metric is actually AE (asymptotically Euclidean), our formula not only implies a positive mass theorem for Kahler metrics, but also yields a Penrose-type inequality for the mass.
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