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Donaldson’s Q-operators for symplectic manifolds

Abstract

We prove an estimate for Donaldson’s Q-operator on a prequantized compact symplectic manifold. This estimate is an ingredient in the recent result of Keller and Lejmi (2017) about a symplectic generalization of Donaldson’s lower bound for the L 2-norm of the Hermitian scalar curvature.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11401232 and 11528103), Agence nationale de la recherche (Grant No. ANR-14-CE25-0012-01), funded through the Institutional Strategy of the University of Cologne within the German Excellence Initiative and Deutsche Forschungsgemeinschaft Funded Project Sonderforschungsbereich Transregio 191.

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Correspondence to Xiaonan Ma.

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In memory of Professor LU QiKeng (1927–2015)

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Lu, W., Ma, X. & Marinescu, G. Donaldson’s Q-operators for symplectic manifolds. Sci. China Math. 60, 1047–1056 (2017). https://doi.org/10.1007/s11425-016-9047-6

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  • DOI: https://doi.org/10.1007/s11425-016-9047-6

Keywords

  • Q-operator
  • quantization
  • symplectic manifold

MSC(2010)

  • 53D50