Abstract
In this survey, we discuss the geodesic problem in the space of Kähler potentials and its applications to constant scalar curvature Kähler (cscK) metrics. We start with the geometrical picture discovered by Mabuchi (1987), Donaldson (1999) and Semmes (1992), and then discuss the background and recent progress on the geodesic problem. Finally, we discuss the application of the geodesics to the existence and uniqueness of cscK metrics.
| Translated title of the contribution | A bird’s eye view on geodesic problems in the space of Kähler potentials |
|---|---|
| Original language | Chinese (Traditional) |
| Pages (from-to) | 115-130 |
| Number of pages | 16 |
| Journal | Scientia Sinica Mathematica |
| Volume | 55 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 2025 |
Keywords
- constant scalar curvature Kähler metric
- geodesic
- space of Kähler potentials
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