椭圆Galerkin的引力透镜和Schwarz函数
Gravitational lensing by Elliptical Galaxies, and the Schwarz Function
摘要：
本文讨论了具有某些特殊质量分布的椭圆星系的引力透镜。使用简单的技术，从理论的正交域和施瓦茨函数（cf。\cite{Sh}）我们证明了当共焦椭圆上的质量密度恒定时，点源的透镜像总数不超过5（4个亮像和1个暗像）。此外，使用潜水-Nikliborc逆著名的牛顿定理关于潜在的椭圆体，我们表明，“爱因斯坦环”必须始终是圆（在没有潮汐剪切），或椭圆。
英文摘要：
We discuss gravitational lensing by elliptical galaxies with some particular mass distributions. Using simple techniques from the theory of quadrature domains and the Schwarz function (cf. \cite{Sh}) we show that when the mass density is constant on confocal ellipses, the total number of lensed images of a point source cannot exceed 5 (4 bright images and 1 dim image). Also, using the Dive--Nikliborc converse of the celebrated Newton's theorem concerning the potentials of ellipsoids, we show that ``Einstein rings'' must always be either circles (in the absence of a tidal shear), or ellipses.
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