Advances in Complex Geometry.

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.

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 articles devoted to various aspects of the theory of complex manifolds and functions on such manifolds.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.