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Comparison theorems for GJMS operators

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Abstract

In this paper, we compare the first order fractional GJMS (see Graham et al. (1992)) operator P1 with the conformal Laplacian P2, on the conformal infinity of a Poincaré-Einstein manifold. We derive some inequalities between the Yamabe constants and the first eigenvalues associated with P1 and P2, and prove some rigidity theorems by characterizing the equalities. Similarly, some comparison theorems between P2 and the Paneitz operator P4 or the 6th order GJMS operator P6 are also given.

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Acknowledgements

The first author was supported by National Natural Science Foundation of China (Grant Nos. 11871331 and 11571233). The second author was supported by National Natural Science Foundation of China (Grant No. 11871331). The first author thanks Professor Sun-Yung Alice Chang for helpful discussions on this topic.

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China

    Fang Wang & Huihuang Zhou

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  1. Fang Wang
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  2. Huihuang Zhou
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Correspondence to Fang Wang.

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Wang, F., Zhou, H. Comparison theorems for GJMS operators. Sci. China Math. 64, 2479–2494 (2021). https://doi.org/10.1007/s11425-020-1689-1

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  • DOI: https://doi.org/10.1007/s11425-020-1689-1

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