Laplacian Vanishing Theorem for Quantized Singular Liouville Equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913568139509760 |
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| author | Wei, Juncheng Zhang, Lei |
| author_facet | Wei, Juncheng Zhang, Lei |
| contents | In this article we establish a vanishing theorem for singular Liouville equation with quantized singular source. If a blowup sequence tends to infinity near a quantized singular source and the blowup solutions violate the spherical Harnack inequality around the singular source (non-simple blow-ups), the Laplacian of a coefficient function must tend to zero. This seems to be the first second order estimates for Liouville equation with quantized sources and non-simple blow-ups. This result as well as the key ideas of the proof would be extremely useful for various applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_10825 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Laplacian Vanishing Theorem for Quantized Singular Liouville Equation Wei, Juncheng Zhang, Lei Analysis of PDEs 35J61, 35J75 In this article we establish a vanishing theorem for singular Liouville equation with quantized singular source. If a blowup sequence tends to infinity near a quantized singular source and the blowup solutions violate the spherical Harnack inequality around the singular source (non-simple blow-ups), the Laplacian of a coefficient function must tend to zero. This seems to be the first second order estimates for Liouville equation with quantized sources and non-simple blow-ups. This result as well as the key ideas of the proof would be extremely useful for various applications. |
| title | Laplacian Vanishing Theorem for Quantized Singular Liouville Equation |
| topic | Analysis of PDEs 35J61, 35J75 |
| url | https://arxiv.org/abs/2202.10825 |