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Explore quantitative isoperimetric inequalities and their applications to capillarity problems in this 37-minute mathematical lecture delivered by Marco Pozzetta at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into advanced mathematical concepts connecting geometric measure theory with physical phenomena involving surface tension and fluid interfaces. Learn how isoperimetric inequalities, which relate the volume of geometric shapes to their surface area, can be quantified and applied to understand capillary effects in various physical systems. Examine the mathematical framework that governs the behavior of liquid drops, soap films, and other capillary phenomena through rigorous analytical techniques. This presentation was delivered as part of the comprehensive Thematic Programme on "Free Boundary Problems," providing insights into cutting-edge research at the intersection of pure mathematics and mathematical physics.
