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Explore geometric variational methods and their applications to curvature problems in this 49-minute lecture by Chao Li from NYU's Courant Institute. Delve into the Schoen-Yau dimension descent approach for scalar curvature problems and examine recent extensions with applications to various curvature conditions. Gain insights into how minimal surfaces and other geometric variational problems contribute to the study of curvature in mathematics. This talk, presented at the Institut des Hautes Etudes Scientifiques (IHES), offers a comprehensive review of these advanced mathematical concepts and their implications in the field of differential geometry.
