Rounding corners of gearlike domains and the omitted area problem (Q5903044)

This is an eminently readable account of the history of progress on the Bieberbach conjecture from Koebe and Bieberbach, through Loewner, Lebedev and Milin, to its recent proof by Louis de Branges - in a most outstanding way. The conjecture was that if the function \(f(z)=z+a_ 2z^ 2+..\). is analytic and univalent (that is, one-one) in \(| z| <1\), then \(| a_ n| \leq n\).