Green function rigidity for two dimensional sphere
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909983381127168 |
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| author | Lai, Mijia Zhang, Chilin |
| author_facet | Lai, Mijia Zhang, Chilin |
| contents | We verify a conjecture proposed by X. Chen and Y. Shi, which arises from their study of the Green function on spheres in Euclidean space. More precisely, let $M\subset \mathbb{R}^3$ be a closed $C^{2}$ embedded surface and suppose that there exists a point $p\in M$ so that its Green function $G$ is of the form $G(p,q)=-\frac{1}{2π} \ln d_{\mathbb{R}^3}(p,q)+c, \forall q\neq p$, then $M$ must be a round sphere. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_03773 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Green function rigidity for two dimensional sphere Lai, Mijia Zhang, Chilin Differential Geometry Analysis of PDEs We verify a conjecture proposed by X. Chen and Y. Shi, which arises from their study of the Green function on spheres in Euclidean space. More precisely, let $M\subset \mathbb{R}^3$ be a closed $C^{2}$ embedded surface and suppose that there exists a point $p\in M$ so that its Green function $G$ is of the form $G(p,q)=-\frac{1}{2π} \ln d_{\mathbb{R}^3}(p,q)+c, \forall q\neq p$, then $M$ must be a round sphere. |
| title | Green function rigidity for two dimensional sphere |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2601.03773 |