UBC Theses and Dissertations
Selfduality in geometry : Yang-Mills connections and selfdual lagrangians Donaldson, Jason Roderick
The convex theory of selfdual Lagrangians recently developed by Ghoussoub analyses junctionals rooted in an expanse of partial differential equations and finds their minima not variationally but rather by realizing that they assume a prescribed lower bound. This is exactly the circumstance in the selfdual and anti-selfdual Yang-Mills equations that arise in the physical field theory and the study of the geometric and topological structure of four-dimensional manifolds. I expose the Yang-Mills equations, building up the geometry from student-level and subsequently outline the setting of selfdual Lagrangians. The theories are clearly analogous and the last section feints at the exact link.
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