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arXiv · 2109.02014

Scattering on singular Yamabe spaces

Sun-Yung Alice Chang·Stephen E. McKeown·Paul Yang
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Abstract

We apply scattering theory on asymptotically hyperbolic manifolds to singular Yamabe metrics, applying the results to the study of the conformal geometry of compact manifolds with boundary. In particular, we define extrinsic versions of the conformally invariant powers of the Laplacian, or GJMS operators, on the boundary of any such manifold, along with associated extrinsic Q-curvatures. We use the existence and uniqueness of a singular Yamabe metric to define also nonlocal extrinsic fractional GJMS operators on the boundary, and draw other global conclusions about the scattering operator, including a Gauss-Bonnet theorem in dimension four.

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Sun-Yung Alice Chang, Stephen E. McKeown, Paul Yang. 2021-09-05. Scattering on singular Yamabe spaces. https://arxiv.org/abs/2109.02014

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