Rigidity of complete Kähler-Einstein metrics under cscK perturbations
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908958796546048 |
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| author | Sha, Zehao |
| author_facet | Sha, Zehao |
| contents | In this paper, we study constant scalar curvature Kähler (cscK) metrics on complete non-compact Kähler--Einstein manifolds. We give sufficient conditions under which a cscK perturbation of a Kähler--Einstein metric must remain Kähler--Einstein. As a model case, we prove that the Bergman metric on a bounded strictly pseudoconvex domain is Kähler--Einstein whenever it has constant scalar curvature. In particular, combined with Huang--Xiao's resolution of Cheng's conjecture, this yields the ball characterization for smooth bounded strictly pseudoconvex domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13278 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of complete Kähler-Einstein metrics under cscK perturbations Sha, Zehao Differential Geometry Complex Variables In this paper, we study constant scalar curvature Kähler (cscK) metrics on complete non-compact Kähler--Einstein manifolds. We give sufficient conditions under which a cscK perturbation of a Kähler--Einstein metric must remain Kähler--Einstein. As a model case, we prove that the Bergman metric on a bounded strictly pseudoconvex domain is Kähler--Einstein whenever it has constant scalar curvature. In particular, combined with Huang--Xiao's resolution of Cheng's conjecture, this yields the ball characterization for smooth bounded strictly pseudoconvex domains. |
| title | Rigidity of complete Kähler-Einstein metrics under cscK perturbations |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2510.13278 |