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arXiv · 0909.3207

Spectral characterization of Poincaré-Einstein manifolds with infinity of positive Yamabe type

Colin Guillarmou·Jie Qing
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Abstract

In this paper, we give a sharp spectral characterization of conformally compact Einstein manifolds with conformal infinity of positive Yamabe type in dimension $n+1>3$. More precisely, we prove that the largest real scattering pole of a conformally compact Einstein manifold $(X,g)$ is less than $\ndemi -1$ if and only if the conformal infinity of $(X,g)$ is of positive Yamabe type. If this positivity is satisfied, we also show that the Green function of the fractional conformal Laplacian $P(α)$ on the conformal infinity is non-negative for all $α\in [0, 2]$.

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Colin Guillarmou, Jie Qing. 2009-09-17. Spectral characterization of Poincaré-Einstein manifolds with infinity of positive Yamabe type. https://arxiv.org/abs/0909.3207

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