Uniform estimates of Green functions and Sobolev-type inequalities on real and complex manifolds
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914959896608768 |
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| author | Deng, Fusheng Huang, Gang Qin, Xiangsen |
| author_facet | Deng, Fusheng Huang, Gang Qin, Xiangsen |
| contents | We prove certain $L^p$ Sobolev-type and Poincaré-type inequalities for functions on real and complex manifolds for the gradient operator $\nabla$, the Laplace operator $Δ$, and the operator $\bar\partial$.
Integral representations for functions are key to get such inequalities. The proofs of the main results involves certain uniform estimates for the Green functions and their gradients on Riemannian manifolds, which are also established in the present work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19353 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform estimates of Green functions and Sobolev-type inequalities on real and complex manifolds Deng, Fusheng Huang, Gang Qin, Xiangsen Complex Variables Differential Geometry We prove certain $L^p$ Sobolev-type and Poincaré-type inequalities for functions on real and complex manifolds for the gradient operator $\nabla$, the Laplace operator $Δ$, and the operator $\bar\partial$. Integral representations for functions are key to get such inequalities. The proofs of the main results involves certain uniform estimates for the Green functions and their gradients on Riemannian manifolds, which are also established in the present work. |
| title | Uniform estimates of Green functions and Sobolev-type inequalities on real and complex manifolds |
| topic | Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2409.19353 |