Universal Kobayashi-Hitchin Correspondence on Hermitian Manifolds.

Intro -- Contents -- Chapter 1. Introduction -- Chapter 2. The finite dimensional Kobayashi-Hitchin correspondence -- 2.1. Analytic Stability, Symplectic stability -- 2.2. The Continuity Method in the finite dimensional case -- 2.3. Maximal weight functions for linear and projective actions -- Chapter 3. A "universal" complex geometric classification problem -- 3.1. Oriented holomorphic pairs -- 3.2. The stability condition for universal oriented holomorphic pairs -- Chapter 4. Hermitian-Einstein pairs -- 4.1. The Hermitian-Einstein equation -- 4.2. Pairs which allow Hermitian-Einstein reductions are polystable -- Chapter 5. Polystable pairs allow Hermitian-Einstein reductions -- 5.1. The perturbed equation -- 5.2. A priori estimates for the solution s[sub(ε)] -- 5.3. Solving the equation (e[sub(ε)]) for ε ∈ ( 0,1] -- 5.4. Destabilizing the pair in the unbounded case -- Chapter 6. Examples and Applications -- 6.1. Oriented holomorphic principal bundles and oriented connections -- 6.2. Moduli spaces of oriented pairs -- 6.3. Non-abelian monopoles on Gauduchon surfaces -- Chapter 7. Appendix -- 7.1. Chern connections -- 7.2. Orbits of the adjoint action, sections in the adjoint bundle -- 7.3. Local maximal torus reductions of a K-bundle -- 7.4. Connection and maximal torus reductions -- 7.5. Analytic results -- 7.6. Weakly holomorphic parabolic reductions -- Bibliography.

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