Author | Siu, Yum-Tong. author |
---|---|
Title | Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kรคhler-Einstein Metrics [electronic resource] : Delivered at the German Mathematical Society Seminar in Dรผsseldorf in June, 1986 / by Yum-Tong Siu |
Imprint | Basel : Birkhรคuser Basel, 1987 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-7486-1 |
Descript | 172 p. online resource |
1. The heat equation approach to Hermitian-Einstein metrics on stable bundles -- ยง1. Definition of Hermitian-Einstein metrics -- ยง2. Gradient flow and the evolution equation -- ยง3. Existence of solution of evolution equation for finite time -- ยง4. Secondary characteristics -- ยง5. Donaldsonโs functional -- ยง6. The convergence of the solution at infinite time -- Appendix A. Hermitian-Einstein metrics of stable bundles over curves -- Appendix B. Restriction of stable bundles -- 2. Kรคhler-Einstein metrics for the case of negative and zero anticanonical class -- ยง1. Monge-Ampรจre equation and uniqueness -- ยง2. Zeroth order estimates -- ยง3. Second order estimates -- ยง4. Hรถlder estimates for second derivatives -- ยง5. Derivation of Harnack inequality by Moserโs iteration technique -- ยง6. Historical note -- 3. Uniqueness of Kรคhler-Einstein metrics up to biholomorphisms -- ยง1. The role of holomorphic vector fields -- ยง2. Proof of Uniqueness -- ยง3. Computation of the Differential. -- ยง4. Computation of the Hessian -- Appendix A. Lower bounds of the Greenโs function of Laplacian -- 4. Obstructions to the Existence of Kรคhler-Einstein Metrics -- ยง1. Reductivity of automorphism group -- ยง2. The obstruction of Kazdan-Warner -- ยง3. The Futaki invariant -- 5. Manifolds with suitable finite symmetry -- ยง1. Motivation for the use of finite symmetry -- ยง2. Relation between supM? and infM? -- ยง3. Estimation of m+?? -- ยง4. The use of finite group of symmetry -- ยง5. Applications -- References