带权Quadrature域的点源平衡问题
Point Source Equilibrium Problems with Connections to Weighted Quadrature Domains
摘要：
我们探讨平衡测度和正交恒等式的支持之间的联系，特别是在点源的情况下，添加到外部场$Q(z)=|z|^{2p}$与$p \in \mathbb{N}$。在此过程中，我们描述了一些关于加权面积测度$|z|^{2p}dA_z$和复边界测度$|z|^{-2p}dz$的求积域。
英文摘要：
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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