Chapter 5

Plurisubharmonic functions and positive currents870EA66136BC

Local plurisubharmonic functions, weak positivity, and plurifine geometry.

Sections and subsections

1. 5.1 Complex differential forms and positive currents4DEEEF894245
2. 5.2 Complex manifolds and differential formsD8E2D1A98ACF
3. 5.3 Currents and positivityACB622806098
4. 5.4 Local potentials for closed (1,1)-currents618FE2108D26
5. 5.5 Holomorphic zeros and the Poincaré–Lelong formula0C34F7796300
6. 5.6 Maps of currents and local mass9F1C9C4A649E
7. 5.7 Plurisubharmonic functions7B39B08A9568
8. 5.8 The line definition and upper semicontinuity55393AEE99C8
9. 5.9 Positive Hessians and holomorphic maps484A05EF6DF1
10. 5.10 Limits, envelopes and local integrability5C7282E51B13
11. 5.11 Extension across closed exceptional setsE197EAFECEC0
12. 5.12 Kiselman's minimum principle53A48113C242
13. 5.13 The definition of plurisubharmonic functions92A4FA45DFE1
    1. 5.13.1 The $1$-dimensional case600FCCB417C9
    2. 5.13.4 The higher dimensional caseEB9F157B42F2
    3. 5.13.13 The manifold case7BAC2CC7335C
14. 5.14 Properties of plurisubharmonic functions6C47792FE6D9
15. 5.15 Plurifine topologyDFFF533F1AE8
    1. 5.15.1 Plurifine topology on domainsC9F4423A543A
    2. 5.15.17 Plurifine topology on manifolds2403FAC7083C
16. 5.16 Lelong numbers and multiplier ideal sheavesEB678D619AD9
17. 5.17 Quasi-plurisubharmonic functions4DF694F99750
18. 5.18 Analytic singularities26AEEBDF865B
19. 5.19 The space of currentsEB85809E6CA8
20. 5.20 Plurisubharmonic metrics on line bundlesA59F8B8F06A8
21. 5.21 Plurisubharmonic functions and singularitiesEDB5A2485B58
22. 5.22 Plurisubharmonic potentials17A37A0D3690
23. 5.23 Changes of background012278DBB6E8
24. 5.24 Maxima and the maximum principleAA6F3BC0AD9F
25. 5.25 Normalized compactness0B216F0B911E
26. 5.26 Uniform exponential integrability5A19CE5C3CCE
27. 5.27 Local products and capacity5E507B6993DC
    1. 5.27.13 Polar parts on curves1953F5546AC6
    2. 5.27.17 Products at small pole sets486795BA5E5C
    3. 5.27.20 Sobolev regularity at divisorial polesC37C319849E5
    4. 5.27.25 Spherical Monge–Ampère measuresC95109EA4FF8
    5. 5.27.27 Measure concentration under integrable convergence4FE21E50E832
    6. 5.27.32 Adding a prescribed local measure38F5E7BC8433
    7. 5.27.37 Full cluster sets at the zero potentialC9D7C212A8BF
    8. 5.27.40 Cluster sets at a bounded backgroundA72166484AB2
28. 5.28 Products with smooth backgrounds5E2B332B89B4
29. 5.29 Hermitian capacityDD310AD8B258
    1. 5.29.1 Capacity estimates1C5C06D2C5D9
    2. 5.29.6 Integration against a Hölder referenceCACF6025C681
    3. 5.29.11 Capacity bounds for Hölder references510FD09C306A
    4. 5.29.14 Convergence of potentials and measures97C040D849DD
    5. 5.29.21 Vanishing area on curvesB092BD05E335
30. 5.30 Comparing local regularizationsDB8E63271D73
31. 5.31 Gluing with a small curvature error78243032B1A1
32. 5.32 Regularization in a fixed Hermitian background26C061D9E9B2
33. 5.33 Singularity type and multiplier ideals9A10411F1BCD
34. 5.34 Analytic types and restriction0D77FC17B23B
    1. 5.34.2 Lelong level setsE911F3E2C8E9
35. 5.35 The local Bergman estimates51F374296336
36. 5.36 The global curvature bound3BCA55154463
    1. 5.36.3 Regularization of closed currentsD4C469F61056
    2. 5.36.4 Smooth remainders after resolution70049B9396E7
37. 5.37 Multiplier ideals and logarithmic poles5BB7B3EA169D
    1. 5.37.9 Weighted distance from a sum of multiplier ideals1B01826812A9
    2. 5.37.17 The optimal constant in dimension oneA5A50BF6024B
    3. 5.37.24 Distance for several hyperplane weightsA632F1B7CA50
38. 5.38 Lelong numbers and divisorial estimates2C2417A75DF4
39. 5.39 Potential regularity and metric distanceDE3129821F10
    1. 5.39.4 Dini moduli and limits of distances4B8CF50FE6DC
40. 5.40 Obstacle envelopes8EA2EE30DE99
    1. 5.40.9 A hyperplane Green envelope on the ball765486939AA3
41. 5.41 The minimum principle392B79314DF8
    1. 5.41.4 Pointwise Legendre transforms63DEBF0DF568
42. 5.42 Chern-connection regularization001730C9ED64
    1. 5.42.3 The general curvature modulus45B2E87FDE47
    2. 5.42.6 Hölder reference approximation and weighted smoothing91A88ECF3F18
    3. 5.42.9 A linear error for a smooth background23459D626290
43. 5.43 Pullback and descent88AEFA5005B9
    1. 5.43.1 Holomorphic disks1F1A3CC0946E
    2. 5.43.3 Compact fibersA5D491DF2CA3
    3. 5.43.6 Maps to a curve3110CB46064E
    4. 5.43.12 The curve of fiber components35C176E64D5B
    5. 5.43.14 Finite maps between curves1C4BCE809D00
    6. 5.43.17 ModificationsD643D283EFB3
    7. 5.43.21 Multiplier ideals under modificationsF75CE9F0BB10
    8. 5.43.25 Restriction of analytic approximantsB669E8E3479E
44. 5.44 Integration against non-pluripolar measures2111608E9FA1
    1. 5.44.1 A fixed measure48FF0BFC07F6
    2. 5.44.3 Vanishing exponents7442B45F8567
    3. 5.44.6 Measures with bounded potentials80117515F812
    4. 5.44.9 Smoothing the measure37976A2408E0
45. 5.45 Curvature of line bundles355A31F789F6
46. 5.46 Polar curvatureAFA07BFD0E7B
47. 5.47 Pluripolar sets and the plurifine topologyF5A3147592B6
    1. 5.47.1 Pluripolar sets and relative extremal functions27FCEC6F336F
    2. 5.47.9 Global poles on Euclidean spaceAE92E4DE9A4F
    3. 5.47.13 Thinness and plurifine neighborhoods333115F369F9
    4. 5.47.19 Countable selections and plurifine locality03B3029EB4B3
    5. 5.47.24 Common poles and quasi-extrema6AAE49F7183F