The structure of fully nonlinear equations and its applications to prescribed problems on complete conformal metrics
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910890319675392 |
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| author | Yuan, Rirong |
| author_facet | Yuan, Rirong |
| contents | This paper investigates the structure of fully nonlinear equations and their applications to geometric problems. We solve some fully nonlinear version of the Loewner-Nirenberg and Yamabe problems. Notably, we introduce Morse theory techniques to construct admissible metrics under a weak condition on the underlying metric, which can be further relaxed in a broad setting. Furthermore, we provide some topological obstruction to demonstrate the optimality of our structural conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18757 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The structure of fully nonlinear equations and its applications to prescribed problems on complete conformal metrics Yuan, Rirong Analysis of PDEs Differential Geometry This paper investigates the structure of fully nonlinear equations and their applications to geometric problems. We solve some fully nonlinear version of the Loewner-Nirenberg and Yamabe problems. Notably, we introduce Morse theory techniques to construct admissible metrics under a weak condition on the underlying metric, which can be further relaxed in a broad setting. Furthermore, we provide some topological obstruction to demonstrate the optimality of our structural conditions. |
| title | The structure of fully nonlinear equations and its applications to prescribed problems on complete conformal metrics |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2503.18757 |