A factorization of the GJMS operators of special Einstein products and applications

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2024-11-03 DOI:10.1112/jlms.70023

Jeffrey S. Case, Andrea Malchiodi

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引用次数: 0

Abstract

We show that the GJMS operators of a special Einstein product factor as a composition of second- and fourth-order differential operators. In particular, our formula applies to the Riemannian product $H^{ℓ} \times S^{d - ℓ}$ . We also show that there is an integer $D = D (k, ℓ)$ such that if $d ⩾ D$ , then for any special Einstein product $N^{ℓ} \times M^{d - ℓ}$ , the Green's function for the GJMS operator of order $2 k$ is positive. As a result, these products give new examples of closed Riemannian manifolds for which the $Q_{2 k}$ -Yamabe problem is solvable.

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特殊爱因斯坦积的 GJMS 算子因式分解及其应用

我们证明，特殊爱因斯坦积的 GJMS 算子因子是二阶和四阶微分算子的组合。特别是，我们的公式适用于黎曼积 H ℓ × S d - ℓ $H^{\ell }。\times S^{d-\ell }$ 。我们还证明，存在一个整数 D = D ( k , ℓ ) $D = D(k,\ell)$ ，如果 d ⩾ D $d \geqslant D$，那么对于任何特殊的爱因斯坦积 N ℓ × M d - ℓ $N^\ell \times M^{d-\ell }$，阶数为 2 k $2k$ 的 GJMS 算子的格林函数为正。因此，这些乘积给出了Q 2 k $Q_{2k}$ -Yamabe问题可解的封闭黎曼流形的新例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.