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arXiv · 2202.10825

Laplacian Vanishing Theorem for Quantized Singular Liouville Equation

Juncheng Wei·Lei Zhang
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Abstract

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.

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Juncheng Wei, Lei Zhang. 2022-02-22. Laplacian Vanishing Theorem for Quantized Singular Liouville Equation. https://arxiv.org/abs/2202.10825

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