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arXiv · 2203.09421

Point Source Equilibrium Problems with Connections to Weighted Quadrature Domains

Peter D. Dragnev·Alan R. Legg·Edward B. Saff
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Abstract

We explore the connection between supports of equilibrium measures and quadrature identities, especially in the case of point sources added to the external field $Q(z)=|z|^{2p}$ with $p \in \mathbb{N}$. Along the way, we describe some quadrature domains with respect to weighted area measure $|z|^{2p}dA_z$ and complex boundary measure $|z|^{-2p}dz$.

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Peter D. Dragnev, Alan R. Legg, Edward B. Saff. 2022-03-17. Point Source Equilibrium Problems with Connections to Weighted Quadrature Domains. https://arxiv.org/abs/2203.09421

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