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arXiv · 1210.7554

Supports of Weighted Equilibrium Measures: Complete Characterization

Muhammed Ali Alan·Nihat Gokhan Gogus
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Abstract

In this paper, we prove that a compact set $K\subset \mathbb{C}^n$ is the support of a weighted equilibrium measure if and only it is not pluripolar at each of its points extending a result of Saff and Totik to higher dimensions. Thus, we characterize the supports weighted equilibrium measures completely. Our proof is a new proof even in one dimension.

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Muhammed Ali Alan, Nihat Gokhan Gogus. 2012-10-29. Supports of Weighted Equilibrium Measures: Complete Characterization. https://arxiv.org/abs/1210.7554

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