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Explore the mathematical theory of regularity for capillary minimal surfaces in this 34-minute lecture delivered as part of the Thematic Programme on "Free Boundary Problems" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the advanced mathematical concepts surrounding minimal surfaces that arise in capillary phenomena, examining the conditions under which these surfaces exhibit regular behavior and the analytical techniques used to establish such regularity properties. Learn about the intersection of differential geometry, partial differential equations, and free boundary theory as applied to problems involving surface tension and capillary effects, gaining insights into both the theoretical foundations and current research developments in this specialized area of mathematical analysis.
