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MARC 21

Lectures on Hermitian-Einstein metrics for stable bundles and Kahler-Einstein metrics: delivered at the German Mathematical Society seminar in Dusseldorf in June, 1986
Tag	Description
020	$a3-7643-1931-3
080	$a514.764
082	$a516.362
099	$a514.764 SIU
100	$aSiu, Yum-Tong$d1943-
245	$aLectures on Hermitian-Einstein metrics for stable bundles and Kahler-Einstein metrics$bdelivered at the German Mathematical Society seminar in Dusseldorf in June, 1986$cYum-Tong Siu
245	$hM
260	$aBasel$bBirkhäuser$c1987
300	$a171 pages$c24 cm.
440	$aDMV Seminar$v8
520	$a1. The heat equation approach to Hermitian-Einstein metrics on stable bundles.- 1. Definition of Hermitian-Einstein metrics.- 2. Gradient flow and the evolution equation.- 3. Existence of solution of evolution equation for finite time.- 4. Secondary characteristics.- 5. Donaldson's functional.- 6. 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. Kahler-Einstein metrics for the case of negative and zero anticanonical class.- 1. Monge-Ampere equation and uniqueness.- 2. Zeroth order estimates.- 3. Second order estimates.- 4. Hoelder estimates for second derivatives.- 5. Derivation of Harnack inequality by Moser's iteration technique.- 6. Historical note.- 3. Uniqueness of Kahler-Einstein metrics up to biholomorphisms.- 1. The role of holomorphic vector fields.- 2. Proof of Uniqueness.- 3. Computation of the Differential..- 4. Computation of the Hessian.- Appendix A. Lower bounds of the Green's function of Laplacian.- 4. Obstructions to the Existence of Kahler-Einstein Metrics.- 1. Reductivity of automorphism group.- 2. The obstruction of Kazdan-Warner.- 3. The Futaki invariant.- 5. Manifolds with suitable finite symmetry.- 1. Motivation for the use of finite symmetry.- 2. Relation between supM? and infM?.- 3. Estimation of m+??.- 4. The use of finite group of symmetry.- 5. Applications.- References.