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Singular Solutions of the Liouville Equation in a Punctured Disc

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Abstract

A family of radial and non-radial singular solutions of the Liouville equation in a punctured disc is constructed via the fixed point argument. To construct the singular solutions, we need to understand the prescribed asymptotic expansions at the isolated singular point of a singular solution for the Liouville equation.

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Acknowledgements

The authors would like to thank the referee for the careful reading and the valuable and useful suggestions, which greatly improved the manuscript. The research of the first author is supported by NSFC (Nos. 11171092, 11571093), the research of the second author is supported by NSFC (No. 11971147) and CPSF (No. 2019M662475).

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Authors and Affiliations

  1. Department of Mathematics, Henan Normal University, Xinxiang, 453007, China

    Zongming Guo

  2. School of Mathematics and Statistics, Henan University, Kaifeng, 475004, China

    Zhongyuan Liu

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  1. Zongming Guo
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  2. Zhongyuan Liu
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Correspondence to Zhongyuan Liu.

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Guo, Z., Liu, Z. Singular Solutions of the Liouville Equation in a Punctured Disc. J Geom Anal 32, 26 (2022). https://doi.org/10.1007/s12220-021-00764-4

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  • DOI: https://doi.org/10.1007/s12220-021-00764-4

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