Chapter 15

Monge–Ampère equations with prescribed singularitiesEAB08B331BC2

Sections and subsections

1. 15.1 Equations with prescribed singularitiesF9AE3BF05078
2. 15.2 Domination with a smaller background2ACF52860663
3. 15.3 Bounded equations in a semipositive big background9F0629AA9014
   1. 15.3.2 The exponential equation0853ABB454FC
   2. 15.3.4 The normalized equation727A21D220CE
4. 15.4 A quantitative stability estimateB4FB50E0C9DE
5. 15.5 Hölder continuity from bounded stabilityBDF9BACE965B
   1. 15.5.3 Regularity for a measure with a Hölder reference9A0897CE06B0
6. 15.6 Local continuity in a semipositive big backgroundFF4EC5CCEA0B
7. 15.7 Homogeneous replacement on a coordinate ball35C79FB822EF
8. 15.8 Contact support in a big backgroundACC753805E21
   1. 15.8.3 Quasi-continuous obstacles5E57580F8E39
9. 15.9 Compactness with a common lower barrierD6040BDF0454
10. 15.10 A bounded subsolution theorem898B7B54B3D0
11. 15.11 Adding weighted Monge–Ampère measures7BAAE1AD9F47
12. 15.12 Equations in a prescribed ordinary typeC6737BA51F0E
    1. 15.12.5 Existence for a positive exponent3EFAC1693CBD
    2. 15.12.6 The normalized equation21A9095B1925
13. 15.13 Comparison above a strict singular barrier1FCAFCAE9C0E
14. 15.14 Subsolutions and the Gauduchon trace8C0AAADFFCFC
15. 15.15 Stability above a strict barrierA7C7BC261679
16. 15.16 Minimal singularities in an arbitrary big background5961B4E1812C
17. 15.17 Local Hölder continuity in a big background1A5D83E43B0A
    1. 15.17.2 Limits of normalized exponential solutionsB0C9769ACDCD
18. 15.18 Interior smoothness on the regular locus899B82DE5E84
    1. 15.18.2 Local comparison7A246CDE0880
    2. 15.18.4 Bounded traces and smoothness5FD96F70C06E
    3. 15.18.7 Smooth exact approximantsE9933083FDD7
    4. 15.18.13 A polynomial boundary trace estimate94BAFACA36D1
    5. 15.18.20 Exact approximationDF626CDAD5D9
    6. 15.18.24 Localization near the nonregular setB0A92E91F8D0
    7. 15.18.34 Derivative estimates and bounded traces163F19CEE4A0
    8. 15.18.49 Proof of the main theorem6E838824045A
19. 15.19 Degenerating semipositive backgrounds28A495F29AAD
    1. 15.19.8 Small resolutions of nodes8C7192C73C68
    2. 15.19.13 Measures and bounded potentials at a nodeDA6098A35E46
    3. 15.19.18 Distances across finitely many contracting regionsF6016CBBF3C5
    4. 15.19.23 Curve areas and radial tube lengths83F8EFD496FF
20. 15.20 Symmetry and the selected projective limit457A6A4C41F4
    1. 15.20.3 The invariant projective solutionD8114BC528BB
    2. 15.20.7 Second derivatives at positive exponentBDDD67E926DC
21. 15.21 Local density and boundary controlD0D15F32906B
    1. 15.21.1 Smooth boundary traces93E0127DCAFF
    2. 15.21.6 A bounded discontinuous potentialAD0BD024C9A0
    3. 15.21.11 Compact gluingAABABE424D5C
22. 15.22 Equations with resolved logarithmic poles3A4DA254E4F4
    1. 15.22.9 Residual mass12F28DB77548
23. 15.23 Minimal singularities on blowups3F1CADE9F6C1
24. 15.24 Representing measures in an ordinary type2BB76C1E3909
25. 15.25 The homogeneous equation with a Hölder reference679A3E78F3EA
26. 15.26 Singular measures on shrinking spheres4BA6AFA61CAA
27. 15.27 Lower mass and solvability for all measures93CEF832AEA2
28. 15.28 Subsolutions for an individual density72CDE5ADD348
    1. 15.28.5 The greatest normalized threshold subsolutionE09A140F700D
    2. 15.28.8 Smooth comparison testsA89D44842BA5
29. 15.29 Gauduchon tests for integrable densities7B44C03D318B
30. 15.30 Exact equations on products with zero lower massFC44870E2A2C
    1. 15.30.5 Closed factors and arbitrary integrable densitiesEB3E71C5CDCB
31. 15.31 Singular measures on products with a curveE01ACE366291
    1. 15.31.2 The logarithmic potential and its measure trace06937C5027C2
    2. 15.31.7 Exponential equations and uniform selection on the curve9002CCE9B34F
    3. 15.31.12 The product equation and its maximal coefficientC004782057EE
32. 15.32 Stability of the subsolution threshold06284CD8A9D4
    1. 15.32.3 Finite sums of densities3DD22F1D6AC3
    2. 15.32.7 Approximation by bounded density roots1BD556522380
    3. 15.32.10 Density roots from a closed factor6436CD7911BD
33. 15.33 Power capacity bounds and threshold equations119B0BE69A7D
    1. 15.33.5 A logarithmic density with critical coefficient oneB8C5C5469618
34. 15.34 Limits of exponential equationsB63DDE7640A4
    1. 15.34.1 A positive limiting exponent00CDC2A31380
35. 15.35 Exponential equations for an individual densityC3635E28D6B1
    1. 15.35.4 An error bound for the scalar limit36B99A272B8F
    2. 15.35.7 Exponential equations at zero threshold49C07144356F
    3. 15.35.11 Solvable exponents and collapse at zero threshold4B9655E85450
    4. 15.35.14 Positive endpoints and one-sided limits44A2CB44D7CB
36. 15.36 Radial selection for integrable densitiesC10FB3AB7407
    1. 15.36.1 Separation and the radial flux870F2FA3F30A
    2. 15.36.4 The normalized limitCE0514438603
    3. 15.36.7 Scalar centering and its moment boundaryC00DFB603383
    4. 15.36.10 Order in the separated classA874D9C61D74
37. 15.37 Relative equations under positive lower mass31A655BFE398
    1. 15.37.3 Equations for finite measures89AC64C97CA7
    2. 15.37.5 DominationF894544905D6
    3. 15.37.8 Domination for extended measures6EC4D5B55F22
    4. 15.37.12 Common envelopes and dominated continuityBD25F1249EB6
    5. 15.37.18 Convergence under a fixed measure905590071E2F
    6. 15.37.20 Moving bounded carrier measures0BEAB476F799
    7. 15.37.25 Convergence with a common envelope997CC67968A6
    8. 15.37.27 General measures in the minimal envelope class0E0ED0471018
    9. 15.37.30 Equations with a model reference1E3C2CEF22BF
    10. 15.37.31 Normalization at exponent zero643A9037F89C
    11. 15.37.33 Nonuniqueness in the minimal envelope classE6EC3A0A407A