پیشرفت‌ها در هندسه پیچیده: سمینار هندسه پیچیده JHU-UMD، ۲۰۱۵-۲۰۱۸، دانشگاه جان هاپکینز، بالتیمور مریلند و دانشگاه مریلند، کالج پارک، مریلند

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. Cover 1 Title page 4 Contents 6 Preface 8 List of seminars 10 Geometric pluripotential theory on Kähler manifolds 12 Preface 14 Part 1. A primer on Orlicz spaces 18 Part 2. Finite energy pluripotential theory on Kähler manifolds 22 Part 3. The Finsler geometry of the space of Kähler potentials 35 Part 4. Applications to Kähler–Einstein metrics 71 Part 5. Appendix 100 Bibliography 110 Local singularities of plurisubharmonic functions 116 1. Introduction 116 2. Preliminaries 118 3. Local solutions of the complex Monge-Ampère equation — basic examples 123 4. Interior estimates 124 5. Local regularity theory 131 6. Singular sets 141 References 152 Pluriharmonics in general potential theories 156 References 179 Orbifold regularity of weak Kähler-Einstein metrics 180 1. Introduction 180 2. Regularity on the orbifold locus 181 3. Orbifold partial resolution 185 4. Further discussions 186 References 188 Analysis of the Laplacian on the moduli space of polarized Calabi-Yau manifolds 190 1. Introduction 190 2. Two Self-Adjoint Extensions of Hodge Laplacian 191 3. Spectrums of Gaffney Extension 193 4. Spectrums of Friedrichs Extension 199 5. Manifolds with Almost Polar Boundary 199 6. Moduli Space of Polarized Calabi-Yau Manifolds 205 7. Self-Adjointness of the Laplacian on Moduli Space 207 8. An Example 208 References 212 On orthogonal Ricci curvature 214 1. Orthogonal Ricci curvature 214 2. Comparison theorems 216 3. Vanishing theorems 217 4. Examples: classical Kähler C-spaces with b2=1 219 5. Examples: projectivized vector bundles 221 6. Structural results 222 References 225 The Anomaly flow on unimodular Lie groups 228 1. Introduction 228 2. The curvature of unitary connections with torsion on Lie groups 231 3. Hull-Strominger systems and Anomaly flows 237 References 246 Pseudoconcave decompositions in complex manifolds 250 References 269 Back Cover 272 Contains contributions from speakers at the 2015-2018 Johns Hopkins University and University of Maryland Complex Geometry Seminar. The book includes a survey article on recent developments in pluripotential theory and its applications to Kahler-Einstein metrics and continues with articles devoted to aspects of the theory of complex manifolds.