Lectures on Hermitian-Einstein metrics for stable bundles and Kähler-Einstein metrics : delivered at the German Mathematical Society Seminar in Düsseldorf in June, 1986

Yum-Tong Siu

[目次]

  • 1. The heat equation approach to Hermitian-Einstein metrics on stable bundles.- x1. Definition of Hermitian-Einstein metrics.- x2. Gradient flow and the evolution equation.- x3. Existence of solution of evolution equation for finite time.- x4. Secondary characteristics.- x5. Donaldson's functional.- x6. 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.- x1. Monge-Ampere equation and uniqueness.- x2. Zeroth order estimates.- x3. Second order estimates.- x4. Holder estimates for second derivatives.- x5. Derivation of Harnack inequality by Moser's iteration technique.- x6. Historical note.- 3. Uniqueness of Kahler-Einstein metrics up to biholomorphisms.- x1. The role of holomorphic vector fields.- x2. Proof of Uniqueness.- x3. Computation of the Differential..- x4. Computation of the Hessian.- Appendix A. Lower bounds of the Green's function of Laplacian.- 4. Obstructions to the Existence of Kahler-Einstein Metrics.- x1. Reductivity of automorphism group.- x2. The obstruction of Kazdan-Warner.- x3. The Futaki invariant.- 5. Manifolds with suitable finite symmetry.- x1. Motivation for the use of finite symmetry.- x2. Relation between supM? and infM?.- x3. Estimation of m+??.- x4. The use of finite group of symmetry.- x5. Applications.- References.

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この本の情報

書名 Lectures on Hermitian-Einstein metrics for stable bundles and Kähler-Einstein metrics : delivered at the German Mathematical Society Seminar in Düsseldorf in June, 1986
著作者等 Deutsche Mathematiker-Vereinigung. Seminar
Siu, Yum-Tong
Siu Y
シリーズ名 DMV seminar
出版元 Birkhäuser Verlag
刊行年月 1987
ページ数 171 p.
大きさ 24 cm
ISBN 3764319313
0817619313
NCID BA01223671
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言語 英語
出版国 スイス
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