@article{6b2ef7fde7504dd29ca5815119d84fed,
title = "Scattering on singular Yamabe spaces",
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 in any conformal class 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.",
keywords = "GJMS, Singular Yamabe, boundary, conformal hypersurface, scattering",
author = "Chang, {Sun Yung Alice} and McKeown, {Stephen E.} and Paul Yang",
note = "Funding Information: The authors found an error in their formula for ck in Section 3 of an earlier draft thanks to an explicit computation in [22], and have corrected it here. Stephen McKeown carried out part of the work while a postdoctoral research associate at Princeton University, whom he thanks for the hospitality and support. The authors warmly thank two anonymous referees for their numerous excellent suggestions. They also thank Aaron Tyrrell and Andreas Juhl, who caught several confusing typos. Sun-Yung Alice Chang and Paul Yang were partially supported by NSF grant DMS-1607091. Stephen E. McKeown was partially supported by NSF RTG grant DMS-1502424. Paul Yang was partially supported by Simons Foundation grant 615589. Funding Information: Funding. Sun-Yung Alice Chang and Paul Yang were partially supported by NSF grant DMS-1607091. Stephen E. McKeown was partially supported by NSF RTG grant DMS-1502424. Paul Yang was partially supported by Simons Foundation grant 615589. Publisher Copyright: {\textcopyright} 2022 Real Sociedad Matem{\'a}tica Espa{\~n}ola Published by EMS Press.",
year = "2022",
doi = "10.4171/RMI/1390",
language = "English (US)",
volume = "38",
pages = "2153--2184",
journal = "Revista Matematica Iberoamericana",
issn = "0213-2230",
publisher = "Universidad Autonoma de Madrid",
number = "7",
}