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Minimal surfaces are ubiquitous in geometry and applied science but their existence theory is rather mysterious. For instance, Yau in 1982 conjectured that any 3-manifold admits infinitely many closed minimal surfaces but the best one knows is the existence of at least three. After a brief historical account, I will talk about my ongoing work with Marques and the progress we made on this question in our recent work with Irie and Song: we showed that for generic metrics, minimal surfaces are dense and equidistributed.
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