Degenerate Complex Monge–Ampère Equations

  • Vincent Guedj

    Université Paul Sabatier, Toulouse, France
  • Ahmed Zeriahi

    Université Paul Sabatier, Toulouse, France
Degenerate Complex Monge–Ampère Equations cover

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FrontmatterDownload pp. i–iv
IntroductionDownload pp. v–xv
ContentsDownload pp. xvii–xxiv
Part I The local theorypp. 1–2
1Plurisubharmonic functionspp. 3–37
2Positive currentspp. 39–74
3The complex Monge–Ampère operatorpp. 75–100
4The Monge–Ampère capacitypp. 101–129
5The Dirichlet problempp. 131–160
6Viscosity solutionspp. 161–187
Part II Pluripotential theory on compact manifoldsp. 189
7Compact Kähler manifoldspp. 191–214
8Quasi-plurisubharmonic functionspp. 215–234
9Envelopes and capacitiespp. 235–255
10Finite energy classespp. 257–285
Part III Solving complex Monge–Ampère equationsp. 287
11The variational approachpp. 289–314
12Uniform a priori estimatespp. 315–342
13The viscosity approachpp. 343–361
14Smooth solutionspp. 363–386
Part IV Singular Kähler–Einstein metricsp. 387
15Canonical metricspp. 389–417
16Singularities and the Minimal Model Programpp. 419–450
17Bibliographypp. 451–467
Indexpp. 469–472