@inproceedings{0ac80d2e70e2434fa1ee8cb295b2f419,

title = "Gravitational lensing by elliptical galaxies, and the Schwarz function",

abstract = "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. [18]) 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.",

author = "Fassnacht, {C. D.} and Charles Keeton and D. Khavinson",

year = "2009",

doi = "10.1007/978-3-7643-9906-1_6",

language = "English (US)",

isbn = "9783764399054",

series = "Trends in Mathematics",

publisher = "Springer International Publishing",

pages = "115--129",

editor = "Bj{\"o}rn Gustafsson and Alexander Vasilev",

booktitle = "Analysis and Mathematical Physics",

note = "International Conference on New trends in harmonic and complex analysis, 2007 ; Conference date: 07-05-2007 Through 12-05-2007",

}