Chapter 17

Energy, geodesics, rays, and test curves8ACCDAB4280C

Relative energy, Perron interpolation, geodesic rays, and Legendre duality.

Sections and subsections

1. 17.1 Relative energy and Perron segmentsBDB8E5100372
2. 17.2 Integration by parts for bounded differencesF694A6981C1D
3. 17.3 Relative Monge–Ampère energyEC60D9ED3C42
4. 17.4 Continuity and compactness3B8286222A1B
5. 17.5 Variational Monge–Ampère equations16614E7E6F9C
   1. 17.5.1 Existence by maximization06665CC7749C
   2. 17.5.16 Uniqueness by concentration of mass096A13B0C62E
   3. 17.5.19 Bounded differences from the referenceE5281BDCDF1F
   4. 17.5.27 Positive mass and bigness1080E9C054BA
   5. 17.5.40 Mixed masses and concavity69E4E21B68CA
6. 17.6 Singularity envelopes at arbitrary mass178F9F7684F6
7. 17.7 Subgeodesics and Perron segments4C4B950F1CFF
8. 17.8 Energy along weak geodesics0753F06C3AFA
9. 17.9 Extremal slopes and long Perron segments66FE6F0ACABE
10. 17.10 Geodesic rays in the space of potentials1E44B710CD7B
    1. 17.10.1 SubgeodesicsF069E255307E
    2. 17.10.19 Geodesics in the space of potentialsBE861874FCE4
    3. 17.10.40 The metrics on the spaces of potentials and rays770FD61FCF7B
11. 17.11 Test curvesBA6AA7598BE3
12. 17.12 The notion of test curves908139B245F5
13. 17.13 Ross–Witt Nyström correspondenceC9D15D724069
14. 17.14 -model test curvesCAE331B64333
15. 17.15 Operations on test curves9D751AA26579
16. 17.16 Perron interpolation and the geodesic equationE4ED60C8BCA5
    1. 17.16.1 Subgeodesics and endpoint bounds8B8AAB4B5DD3
    2. 17.16.5 Perron segments872589A6FBF3
    3. 17.16.8 The smooth product equationA928C3A148CF
    4. 17.16.11 The $L^2$ action and torsionD4C2C057EC75
    5. 17.16.15 Basic finite energy potentials on a Hopf manifold5C818268C38E
    6. 17.16.23 Negative directions of the raw action124D4C83F5E6
    7. 17.16.28 Explicit basic geodesics and singular potentials1DFB5A5992AD
    8. 17.16.31 Model projection and test curves67EBAA104FDD
17. 17.17 Test curves and Legendre dualityD5DBDCE92D6A
    1. 17.17.1 Envelope test curves and rays22C33F2E9103
    2. 17.17.4 Perron maximalityFA178FC8EDED
    3. 17.17.7 Recovering the singularity envelopesDB66318C651A
    4. 17.17.9 A logarithmic pole on the projective line58086AECC383