Sign of Green's function of Paneitz operators and the Q curvature

By Fengbo Hang, Paul Yang. 2014

56 citations recorded by the source corpus.

In a conformal class of metrics with positive Yamabe invariant, we derive a necessary and sufficient condition for the existence of metrics with positive Q curvature. The condition is conformally invariant. We also prove some inequalities between the Green's functions of the conformal Laplacian operator and the Paneitz operator.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a0f4c3941769b60f5c3ae37a77135550e8a1a0e6

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In Applied Mathematics

1. Guozhen Lu
2. Qiaohua Yang
3. Sun‐Yung Alice Chang
4. Jeffrey S. Case
5. Tianling Jin
6. Jingang Xiong

In Mathematical Physics

1. Qiaohua Yang
2. Guozhen Lu
3. Sun‐Yung Alice Chang
4. Jeffrey S. Case

Citations in the corpus

• On Fractional GJMS Operators (2014, result): “Yang [26] have recently taken another perspective on the strong maximum principle for the Paneitz operator, and in particular showed that one only need to assume that Q is semipositive and the Yamabe constant is positive to recover the result of Gursky and Malchiodi [25].”
• Paneitz operators on hyperbolic spaces and high order Hardy-Sobolev-Maz'ya inequalities on half spaces (2019, methodology): “We also refer the reader to the recent works on Sobolev type inequalities for Paneitz operators on compact Riemannian manifolds by Hang and Yang [26, 27, 28].”