The Critical LYZ Equation in Kähler Geometry
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908780387631104 |
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| author | Fu, Jixiang Yau, Shing-Tung Zhang, Dekai |
| author_facet | Fu, Jixiang Yau, Shing-Tung Zhang, Dekai |
| contents | We establish the existence of smooth solutions for the LYZ equation at the critical phase $θ=(n-2)\fracπ{2}$, thereby solving the critical case of a problem posed by Collins-Jacob-Yau and Li concerning the solvability for phase $θ\leq (n-2)\fracπ{2}$. As applications, we solve the 3D Hessian equation $σ_2 = 1$ and the 4D Hessian quotient equation $σ_3 = σ_1$ under weaker assumptions than previously required. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21492 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Critical LYZ Equation in Kähler Geometry Fu, Jixiang Yau, Shing-Tung Zhang, Dekai Differential Geometry Analysis of PDEs Complex Variables We establish the existence of smooth solutions for the LYZ equation at the critical phase $θ=(n-2)\fracπ{2}$, thereby solving the critical case of a problem posed by Collins-Jacob-Yau and Li concerning the solvability for phase $θ\leq (n-2)\fracπ{2}$. As applications, we solve the 3D Hessian equation $σ_2 = 1$ and the 4D Hessian quotient equation $σ_3 = σ_1$ under weaker assumptions than previously required. |
| title | The Critical LYZ Equation in Kähler Geometry |
| topic | Differential Geometry Analysis of PDEs Complex Variables |
| url | https://arxiv.org/abs/2511.21492 |