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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.09393 |
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| _version_ | 1866914153581510656 |
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| author | Wang, Lin Zhu, Miaomiao |
| author_facet | Wang, Lin Zhu, Miaomiao |
| contents | For a complete noncompact Riemannian manifold with nonnegative Ricci curvature, we show that bounded biharmonic functions are constant and the space consists of biharmonic functions with polynomial growth of a fixed rate is finite dimensional. Also, we derive a Weyl type bound for this space. Finally, we present a finite dimensional result for a class of fourth-order operators on $\mathbb{R}^n$ satisfying certain coefficient conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09393 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The qualitative behavior for biharmonic functions on open manifolds Wang, Lin Zhu, Miaomiao Differential Geometry 31A30, 58J05 For a complete noncompact Riemannian manifold with nonnegative Ricci curvature, we show that bounded biharmonic functions are constant and the space consists of biharmonic functions with polynomial growth of a fixed rate is finite dimensional. Also, we derive a Weyl type bound for this space. Finally, we present a finite dimensional result for a class of fourth-order operators on $\mathbb{R}^n$ satisfying certain coefficient conditions. |
| title | The qualitative behavior for biharmonic functions on open manifolds |
| topic | Differential Geometry 31A30, 58J05 |
| url | https://arxiv.org/abs/2511.09393 |