A Survey on Classical Minimal Surface Theory

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Through the telling of the story of the classification of minimal planar domains, the general mathematician may catch a glimpse of the intrinsic beauty of this theory and the authors' perspective of what is happening at this historical moment in a very classical subject. This includes an updated tour through some of the recent advances in the theory, such as Colding-Minicozzi theory, conformal structure of minimal surfaces, the local removable singularity theorem, and uniqueness of Scherk singly periodic minimal surfaces, and outstanding problems and conjectures.