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Explore a 22-minute lecture from the Thematic Programme on "Infinite-dimensional Geometry: Theory and Applications" that delves into the developments of unbalanced optimal transport (OT) in a constrained setting. Begin with foundational concepts of unbalanced OT and the Wasserstein-Fisher-Rao distance, gaining comprehensive insights into the space of measures. Progress through basic constraints and area measures of convex sets to more complex constraints in OT. Master the proof of minimal energy paths existence through the Fenchel-Rockafellar theorem and its implications. Examine Otto's picture version in this context, understanding the geometric perspective of the theory. Connect fundamental concepts with modern advancements in unbalanced, constrained optimal transport during this mathematical exploration presented at the Erwin Schrödinger International Institute for Mathematics and Physics.
