Helicoidal minimal surfaces of prescribed genus
From the reviewer's perspective, this article represents a major contribution to the field of differential geometry. The main result that is stated and proved is ``For every \(g\), there exist genus-\(g\) helicoids in \(\mathbb R^3\).'' The paper is over 100 page in length, due to the fact that many preliminaries and historical results had to be presented, together with all the preparatory work for proving the main result. This makes it accessible to a large audience of researchers in the field of minimal surfaces, including postdoctoral scholars and graduate students. The reviewer would highly recommend including this paper in a special topics graduate course on differential geometry. The presentation is concise, and very rigorous at the same time. This topic has attracted a lot of attention over the past few years, and the research community is already aware of its importance.
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