Chapter 24

Problems in pluripotential theoryF03E578EF455

Research questions, historical context, and bibliographical commentary.

Sections and subsections

1. 24.1 Problems in Hermitian pluripotential theory9226B45701D5
2. 24.2 Threshold equations and singular limitsA1CD1701B975
   1. 24.2.1 Individual density thresholds33D327BAD4E0
   2. 24.2.3 Dual attainment and exact equations23806B61F487
   3. 24.2.4 Regularity of singular solutions228EC8A6CA8D
   4. 24.2.5 Uniqueness and selectionDFEF338E1977
3. 24.3 Positive Gauduchon volume and bigness6CDBB1FBABB2
   1. 24.3.1 Collapse of normalized Gauduchon testsC56273368CE1
4. 24.4 Closed positivity and geometric equations8871793F78BB
   1. 24.4.1 Nef classes, bigness and the Fujiki class806079150C7A
   2. 24.4.4 Positive lower mass and concentrationE1772510D012
   3. 24.4.7 Primitive elliptic bundles148E1DFBEDF1
   4. 24.4.15 Null loci and the singularities of the Chern–Ricci flowF6F63D20E784
   5. 24.4.16 Balanced and pluriclosed metricsB8BA04F9415A
   6. 24.4.23 Pluriclosed metrics under deformation39D58BE832C0
   7. 24.4.29 Morse inequalities and the choice of volumeB20929459DA6
   8. 24.4.32 Oeljeklaus–Toma manifolds68A7CB3104FE
5. 24.5 Closed and twisted classesB3F20D9F0DB0
6. 24.6 Degeneration orders and finite-distance boundaries7B777ACFF4E8
7. 24.7 Weak Gauduchon adjointsC528B286A8D7
8. 24.8 Topologies on singularity types103C284C8243
   1. 24.8.1 Weak convergence and singularity data163A8FDB4B95
   2. 24.8.2 Volume comparison and analytic approximationEB37AB0B2D63
   3. 24.8.3 Polar curvatureB245A62A943C
9. 24.9 Trace realization and recovery1B042D04CEDB
   1. 24.9.2 Recovery of compatible divisor systems5A6D078648B3
10. 24.10 Sections, kernels and the dimension of growth86B65C86A5FA
    1. 24.10.3 Growing vanishing orders on curves5FCA86C5A588
11. 24.11 Equations on singular spacesC6BAF3541DDF