$L^1$-Stability for complex Monge-Ampère equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916860154347520 |
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| author | Liu, Songchen Zhang, Liyou |
| author_facet | Liu, Songchen Zhang, Liyou |
| contents | We first establish the weak stability results for solutions of complex Monge-Ampère equations in relative full mass classes, extending the results known to hold in the full mass class. Building on weak stability, we then prove the $\mathcal{C}^{k,α}$ stability of solutions to complex Monge-Ampère equations on quasi-projective varieties. As an application, we study the limit of the singular Ricci-flat metrics on $\mathbb{Q}$-Calabi-Yau projective varieties, inspired by Tosatti's work on Calabi-Yau projective manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18392 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $L^1$-Stability for complex Monge-Ampère equations Liu, Songchen Zhang, Liyou Complex Variables Algebraic Geometry Differential Geometry 32U15, 32W20, 32J17, 32Q20 We first establish the weak stability results for solutions of complex Monge-Ampère equations in relative full mass classes, extending the results known to hold in the full mass class. Building on weak stability, we then prove the $\mathcal{C}^{k,α}$ stability of solutions to complex Monge-Ampère equations on quasi-projective varieties. As an application, we study the limit of the singular Ricci-flat metrics on $\mathbb{Q}$-Calabi-Yau projective varieties, inspired by Tosatti's work on Calabi-Yau projective manifolds. |
| title | $L^1$-Stability for complex Monge-Ampère equations |
| topic | Complex Variables Algebraic Geometry Differential Geometry 32U15, 32W20, 32J17, 32Q20 |
| url | https://arxiv.org/abs/2503.18392 |