Scattering on singular Yamabe spaces

Sun Yung Alice Chang, Stephen E. McKeown, Paul Yang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2153-2184
Number of pages32
JournalRevista Matematica Iberoamericana
Volume38
Issue number7
DOIs
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • General Mathematics

Keywords

  • GJMS
  • Singular Yamabe
  • boundary
  • conformal hypersurface
  • scattering

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