Chapter 11

Hermitian geometry, torsion, and Gauduchon duality298536BFFEA2

Torsion, linear mass, traces, weak adjoints, and variational volume.

Sections and subsections

1. 11.1 Torsion and the variation of mass7B453010B5B8
   1. 11.1.1 Integration by parts with a nonclosed formFD6E63098594
   2. 11.1.4 The mass polynomialCA97FF13B1BB
   3. 11.1.11 Mass variation on a complex torusD4D9C4F87D5D
   4. 11.1.15 Comparison and mass invarianceB5345EE28748
   5. 11.1.19 Uniform mass boundsD29B5BFF0A9A
2. 11.2 Monge–Ampère energy and torsion1FC29EAFAA97
   1. 11.2.1 Primitives of the Monge–Ampère one-form49D0776D0F6B
   2. 11.2.6 Radial energy and closed backgroundsB9357DC44463
   3. 11.2.9 First variation in a nonclosed backgroundAEF022344DD6
   4. 11.2.14 Symplectic completions and potential variationsA10584C44FB2
   5. 11.2.22 Completion energy on products of complex toriEF1FC602D899
3. 11.3 Gauduchon metrics and linear mass1009E65ECC4C
4. 11.4 Conformal Gauduchon metrics4ECC3E68F7D5
5. 11.5 Conservation of the trace massA21D56C40154
6. 11.6 The Gauduchon criterion for positivity6029C37CE10F
7. 11.7 Compactness and duality of Gauduchon currentsA532E9A2E94A
8. 11.8 Transverse concentration of Gauduchon tests959649DAC54D
9. 11.9 Convex norms and Gauduchon degrees93399AABE3EC
10. 11.10 Homogeneous convex regularization879A1C19426E
11. 11.11 Strict positivity from the tautological metric733548AD7779
12. 11.12 Polar norms of semipositive Finsler metricsC40892E1279D
13. 11.13 Ample comparison quotients on Hirzebruch surfaces9C2F19628D6F
14. 11.14 Stable extensions approaching the split comparison bundleD9D859664CFB
15. 11.15 Deforming to stable ample bundlesE22565883FFD
16. 11.16 A fixed Stein hypersurface for all Finsler metricsFE1ACFDCD4DA
17. 11.17 Concave neighborhoods and dual norms4276F3B6339D
18. 11.18 Curvature and projective complement exhaustionsF56029D8C19A
19. 11.19 Negative bundle metrics and logarithmic weightsEF53CEC272DE
20. 11.20 External tensor products and complement convexity391E9AF09F50
21. 11.21 Homogeneous plurisubharmonic functions and Hopf complements2ADE48A8B892
22. 11.22 Pluriharmonic currentsB57478F1D4E4
23. 11.23 The adjoint measure of the linearizationC01896004229
    1. 11.23.6 Convex entropies along a Monge–Ampère flow5C3C01BC6D13
    2. 11.23.13 Total variation between two evolving probabilitiesF9C293B132B8
24. 11.24 Fredholm theory for a continuous Hermitian formDB480BD29A98
25. 11.25 Limits of adjoint measures8B86B2B0A308
26. 11.26 Conformal changes and directional curvature positivityA4E01A8B6F30
27. 11.27 Ricci-flat Kähler surfacesFFC070E9C8C2
28. 11.28 Holomorphic sectional curvatureAF4D6581275D
    1. 11.28.6 Rigidity on complex tori61E79198BB98
29. 11.29 Projective first jets and positive bundle metricsA1CB99CAE47B
    1. 11.29.2 The finite-dimensional alternative6243CAB7B202
    2. 11.29.5 Approximation with two derivatives84DD621CC41A
    3. 11.29.8 The metric and measure alternativesB1D39F6DC8D4
30. 11.30 Ramified section tests and a positive root metricEF54BD838F8D
    1. 11.30.2 The weighted family and its first successful level5B78AD45B21A
    2. 11.30.4 Relation to the fixed very ample criterion32E68898DD56
31. 11.31 Gauduchon traces and the topology of potentials15943A2C3613
    1. 11.31.1 The trace map1699E04AE638
    2. 11.31.5 A metric on normalized potentials523982F48F36
    3. 11.31.9 Continuous potentials and pluriharmonic traces951E64D10409
32. 11.32 Normalization and weak adjoint measures7091FEDB43F0
33. 11.33 The scalar functional52D96CD9BFA7
34. 11.34 Supporting probability measuresEE2EC5B3CDE0
    1. 11.34.4 Directional derivativesBD1A1A3DE2D3
    2. 11.34.6 Generic uniqueness39ED4CCC5AE2
    3. 11.34.8 Gauduchon adjoints9E3723511E88
    4. 11.34.10 Continuous positive complex Hessians4C927FD81A61
    5. 11.34.12 Products with a Hermitian factorC277B7427384
    6. 11.34.15 Divisorial smoothingA54217F2E13D
35. 11.35 A convex functional on probability measuresD8DD45551DB2
36. 11.36 Bounded measurable densities and stability0E821D2FEC9D
37. 11.37 Entropy and the closed case694B6AE5D5E5
38. 11.38 Entropy bounds531A2D2A66CF
    1. 11.38.2 The mass bounds as entropy differences7BF91F477A54
    2. 11.38.4 Entropy for a prescribed ordinary type562884633BF8
39. 11.39 Changing the prescribed singularities44DF399743E5
    1. 11.39.2 Uniform comparison of the scalar functionals99DA2DCCD99F
40. 11.40 Varying positive backgroundsABAC4E4BC446
41. 11.41 Divisorial types and moving sections2D3AC831EDA6
    1. 11.41.4 One-sided divisorial classes and sharp thresholds0B775DCEE678
42. 11.42 The mass determined by the functionalF459A353BA9B
43. 11.43 Convex-body criteria for varying references7D0D0E9AC5C3
    1. 11.43.1 Canonical models and their mass6439CBEB8575
    2. 11.43.5 Hausdorff control of the functional3EB28248B606
    3. 11.43.9 A family with nonanalytic isolated poles592E13B7D2ED
    4. 11.43.14 Positive mass with a degenerate smooth residualD4A7E78D4C33
44. 11.44 Selection by a vanishing exponential parameterDB96849B14F8
    1. 11.44.4 A norm defined by the critical scalarA20C27AA8420
    2. 11.44.7 Norming probabilities and integral boundsB51F7B7B7005
    3. 11.44.14 Bounds for the centered potentialsCE46B4F2D02A
    4. 11.44.17 Scalar envelopes of subsolutionsBC341AB6E8A6
45. 11.45 Selection for logarithmic models on productsA167FA614566
    1. 11.45.1 The ordinary model and the greatest solutions27CD354DC77F
    2. 11.45.7 The selected limit with varying dataA00D72781B06
    3. 11.45.12 The critical coefficient and separated orderCEEDD0460992
    4. 11.45.14 Weak adjoints on a product surface2FFAD548CA54
46. 11.46 Residual regularity in radial singularity typesDF55B983AF23
    1. 11.46.1 The prescribed ordinary type31F950502C14
    2. 11.46.7 Density criterion and exact inverse6ECAAB69A33B
    3. 11.46.14 Smooth residuals from flat errors2C18A3499311
    4. 11.46.16 Compact examples and sharp derivative thresholdsFE6A97B82E18
    5. 11.46.19 Smooth residuals with an open density-zero annulus309EDE002FAE
    6. 11.46.21 Products with a zero-lower-mass factor31DB1FA6A441
47. 11.47 Envelopes for singular radial obstaclesAEE10281DB3D
    1. 11.47.3 The convex minorant and its residual2FEAC06EE6DB
    2. 11.47.10 Uniform bounds through moving contactCFB34E7820F0
    3. 11.47.13 The full envelope on a Hermitian productC6C2D9DCA88F