The Mabuchi geometry of low energy classes
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915704949702656 |
|---|---|
| author | Darvas, Tamás |
| author_facet | Darvas, Tamás |
| contents | Let $(X,ω)$ be a Kähler manifold and $ψ: \Bbb R \to \Bbb R_+$ be a concave weight. We show that $\mathcal H_ω$ admits a natural metric $d_ψ$ whose completion is the low energy space $\mathcal E_ψ$, introduced by Guedj-Zeriahi. As $d_ψ$ is not induced by a Finsler metric, the main difficulty is to show that the triangle inequality holds. We study properties of the resulting complete metric space $(\mathcal E_ψ,d_ψ)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_11581 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Mabuchi geometry of low energy classes Darvas, Tamás Differential Geometry Complex Variables Metric Geometry Let $(X,ω)$ be a Kähler manifold and $ψ: \Bbb R \to \Bbb R_+$ be a concave weight. We show that $\mathcal H_ω$ admits a natural metric $d_ψ$ whose completion is the low energy space $\mathcal E_ψ$, introduced by Guedj-Zeriahi. As $d_ψ$ is not induced by a Finsler metric, the main difficulty is to show that the triangle inequality holds. We study properties of the resulting complete metric space $(\mathcal E_ψ,d_ψ)$. |
| title | The Mabuchi geometry of low energy classes |
| topic | Differential Geometry Complex Variables Metric Geometry |
| url | https://arxiv.org/abs/2109.11581 |