Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.02655 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909062698893312 |
|---|---|
| author | Guo, Bin Jian, Wangjian Shi, Yalong Song, Jian |
| author_facet | Guo, Bin Jian, Wangjian Shi, Yalong Song, Jian |
| contents | Let $X$ be a Kähler manifold with semi-ample canonical bundle $K_X$. It is proved by Jian-Shi-Song that for any Kähler class $γ$, there exists $δ>0$ such that for all $t\in (0, δ)$ there exists a unique cscK metric $g_t$ in $K_X+ t γ$. In this paper, we prove that $\{ (X, g_t) \}_{ t\in (0, δ)} $ have uniformly bounded Kähler potentials, volume forms and diameters. As a consequence, these metric spaces are pre-compact in the Gromov-Hausdorff sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02655 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | CscK metrics near the canonical class Guo, Bin Jian, Wangjian Shi, Yalong Song, Jian Differential Geometry Analysis of PDEs 53C55, 35J60 Let $X$ be a Kähler manifold with semi-ample canonical bundle $K_X$. It is proved by Jian-Shi-Song that for any Kähler class $γ$, there exists $δ>0$ such that for all $t\in (0, δ)$ there exists a unique cscK metric $g_t$ in $K_X+ t γ$. In this paper, we prove that $\{ (X, g_t) \}_{ t\in (0, δ)} $ have uniformly bounded Kähler potentials, volume forms and diameters. As a consequence, these metric spaces are pre-compact in the Gromov-Hausdorff sense. |
| title | CscK metrics near the canonical class |
| topic | Differential Geometry Analysis of PDEs 53C55, 35J60 |
| url | https://arxiv.org/abs/2401.02655 |