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On the solutions of the Aubin equation and the K-energy of Einstein–Fano manifolds
We propose an improvement to the bifurcation technique considered by Bando–Mabuchi for the construction of the solutions of the Aubin equation over Einstein–Fano manifolds. We also introduce a simplification in Tian's proof of the properness of the K-energy functional over Einstein–Fano manifolds with trivial holomorphic automorphisms group.