Year: 2021
Author: Fang Wang
Journal of Mathematical Study, Vol. 54 (2021), Iss. 2 : pp. 186–199
Abstract
In this paper, we mainly study the scattering operators for a Poincaré-Einstein manifold $(X^{n+1}, g_+)$, which define the fractional GJMS operators $P_{2\gamma}$ of order $2\gamma$ for $0<\gamma<\frac{n}{2}$ for the conformal infinity $(M, [g])$. We generalise Guillarmou-Qing's positivity results in [8] to the higher order case. Namely, if $(X^{n+1}, g_+)$ $(n\geq 5)$ is a hyperbolic Poincaré-Einstein manifold and there exists a smooth representative $g$ for the conformal infinity such that the scalar curvature $R_g$ is a positive constant and $Q_4$ is semi-positive on $(M, g)$, then $P_{2\gamma}$ is positive for $\gamma\in [1,2]$ and the first real scattering pole is less than $\frac{n}{2}-2$.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v54n2.21.05
Journal of Mathematical Study, Vol. 54 (2021), Iss. 2 : pp. 186–199
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Scattering operators fractional GJMS positivity Poincaré-Einstein.