Coupled continuity equations for constant scalar curvature Kähler metrics
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912818494701568 |
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| author | Shen, Xi Sisi Smith, Kevin |
| author_facet | Shen, Xi Sisi Smith, Kevin |
| contents | Inspired by a parabolic system of Li-Yuan-Zhang and the continuity equation of La Nave-Tian, we study a system of elliptic equations for a Kähler metric $ω$ and a closed $(1, 1)$-form $α$. Assuming a uniform estimate for $ω$, we prove higher order estimates and smooth convergence to a cscK metric coupled to a harmonic $(1, 1)$-form. A simplification of the system is used to recover existence results for Kähler-Einstein metrics when $c_1(X) < 0$. On Riemann surfaces with genus at least $2$, we show smooth convergence to the unique Kähler-Einstein metric from a large class of initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07677 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coupled continuity equations for constant scalar curvature Kähler metrics Shen, Xi Sisi Smith, Kevin Differential Geometry Analysis of PDEs Complex Variables Inspired by a parabolic system of Li-Yuan-Zhang and the continuity equation of La Nave-Tian, we study a system of elliptic equations for a Kähler metric $ω$ and a closed $(1, 1)$-form $α$. Assuming a uniform estimate for $ω$, we prove higher order estimates and smooth convergence to a cscK metric coupled to a harmonic $(1, 1)$-form. A simplification of the system is used to recover existence results for Kähler-Einstein metrics when $c_1(X) < 0$. On Riemann surfaces with genus at least $2$, we show smooth convergence to the unique Kähler-Einstein metric from a large class of initial data. |
| title | Coupled continuity equations for constant scalar curvature Kähler metrics |
| topic | Differential Geometry Analysis of PDEs Complex Variables |
| url | https://arxiv.org/abs/2601.07677 |