Advances in Complex Geometry
This volume contains contributions from speakers at the 2015-2018 joint Johns Hopkins University and University of Maryland Complex Geometry Seminar. It begins with a survey article on recent developments in pluripotential theory and its applications to Kähler-Einstein metrics and continues with art...
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| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
2019
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| Edition: | 1 |
| Series: | Contemporary Mathematics |
| Subjects: | |
| ISBN: | 9781470443337, 1470443333 |
| ISSN: | 0271-4132, 1098-3627 |
| Online Access: | Get full text |
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Table of Contents:
- Geometric pluripotential theory on Kähler manifolds -- Local singularities of plurisubharmonic functions -- Pluriharmonics in general potential theories -- Orbifold regularity of weak Kähler-Einstein metrics -- Analysis of the Laplacian on the moduli space of polarized Calabi-Yau manifolds -- On orthogonal Ricci curvature -- The Anomaly flow on unimodular Lie groups -- Pseudoconcave decompositions in complex manifolds
- Cover -- Title page -- Contents -- Preface -- List of seminars -- Geometric pluripotential theory on Kähler manifolds -- Preface -- Part 1. A primer on Orlicz spaces -- Part 2. Finite energy pluripotential theory on Kähler manifolds -- Part 3. The Finsler geometry of the space of Kähler potentials -- Part 4. Applications to Kähler-Einstein metrics -- Part 5. Appendix -- Bibliography -- Local singularities of plurisubharmonic functions -- 1. Introduction -- 2. Preliminaries -- 3. Local solutions of the complex Monge-Ampère equation - basic examples -- 4. Interior estimates -- 5. Local regularity theory -- 6. Singular sets -- References -- Pluriharmonics in general potential theories -- References -- Orbifold regularity of weak Kähler-Einstein metrics -- 1. Introduction -- 2. Regularity on the orbifold locus -- 3. Orbifold partial resolution -- 4. Further discussions -- References -- Analysis of the Laplacian on the moduli space of polarized Calabi-Yau manifolds -- 1. Introduction -- 2. Two Self-Adjoint Extensions of Hodge Laplacian -- 3. Spectrums of Gaffney Extension -- 4. Spectrums of Friedrichs Extension -- 5. Manifolds with Almost Polar Boundary -- 6. Moduli Space of Polarized Calabi-Yau Manifolds -- 7. Self-Adjointness of the Laplacian on Moduli Space -- 8. An Example -- References -- On orthogonal Ricci curvature -- 1. Orthogonal Ricci curvature -- 2. Comparison theorems -- 3. Vanishing theorems -- 4. Examples: classical Kähler C-spaces with ₂=1 -- 5. Examples: projectivized vector bundles -- 6. Structural results -- References -- The Anomaly flow on unimodular Lie groups -- 1. Introduction -- 2. The curvature of unitary connections with torsion on Lie groups -- 3. Hull-Strominger systems and Anomaly flows -- References -- Pseudoconcave decompositions in complex manifolds -- References -- Back Cover