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On the Coefficients of the Equivariant Szegő Kernel Asymptotic Expansions

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Abstract

Let \((X, T^{1,0}X)\) be a compact connected orientable strongly pseudoconvex CR manifold of dimension \(2n+1\), \(n\ge 1\). Assume that X admits a connected compact Lie group G action and a transversal CR \(S^1\) action, we compute the coefficients of the first two lower-order terms of the equivariant Szegő kernel asymptotic expansions with respect to the \(S^1\) action.

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Authors and Affiliations

  1. Institute of Mathematics, Academia Sinica, Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei, 10617, Taiwan

    Chin-Yu Hsiao

  2. Department of Mathematics, National Central University, Chung-Li, Taoyuan, 32001, Taiwan

    Rung-Tzung Huang

  3. School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, 519082, Guangdong, China

    Guokuan Shao

Authors
  1. Chin-Yu Hsiao
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  2. Rung-Tzung Huang
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  3. Guokuan Shao
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Correspondence to Guokuan Shao.

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Chin-Yu Hsiao was partially supported by Taiwan Ministry of Science and Technology projects 108-2115-M-001-012-MY5 and 109-2923-M-001-010-MY4 and Academia Sinica investigator award. Rung-Tzung Huang was supported by Taiwan Ministry of Science and Technology projects 107-2115-M-008-007-MY2 and 109-2115-M-008-007-MY2. Guokuan Shao was supported by NSFC Grant No. 12001549 and Guangdong Basic and Applied Basic Research Foundation Grant No. 2019A1515110250.

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Hsiao, CY., Huang, RT. & Shao, G. On the Coefficients of the Equivariant Szegő Kernel Asymptotic Expansions. J Geom Anal 32, 31 (2022). https://doi.org/10.1007/s12220-021-00776-0

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  • DOI: https://doi.org/10.1007/s12220-021-00776-0

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