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arXiv · 2607.12859

Comparison Theorems for Fractional GJMS Operators

Huihuang Zhou
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Abstract

In this paper, we mainly focus on the fractional GJMS operators $P_{2\gamma}$ which are defined on the conformal infinity of a Poincar\'{e}-Einstein manifold. We derive two comparison inequalities of the fractional Yamabe constants associated to the fractional GJMS operators. One is between $P_{1}$ and $P_{2\gamma}$ for $\gamma\in (1/2,1)$, and the other is between $P_{2}$ and $P_{2\gamma}$ for $\gamma\in (1,2)$. They both imply the rigidity theorems by characterizing the equalities. Together with the result in \cite{WZ1}, we partially provide some evidence for the monotonicity of the fractional Yamabe constants.

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Huihuang Zhou. 2026-07-14. Comparison Theorems for Fractional GJMS Operators. https://arxiv.org/abs/2607.12859

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