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Summary We present a self-contained and geometric proof of the standard results about maximal compact subgroups of simple Lie groups. The approach follows an idea suggested by Cartan, and is a variant of a proof given by Richardson in the complex case. We apply techniques associated to geometric invariant theory. The main step in the proof involves an argument with Riemannian metrics of nonpositive...
.The main result of the paper is an existence theorem for a constant scalar curvature Kahler metric on a toric surface, assuming the K-stability of the manifold. The proof builds on earlier papers by the author, which reduce the problem to certain a priori estimates. These estimates are obtained using a combination of arguments from Riemannian geometry and convex analysis. The last part of the paper...
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