Scattering on singular Yamabe spaces

Sun-Yung Alice Chang ^[1] ; Stephen E. McKeown ^[2] ; Paul Yang ^[1]
1. [1] Princeton University
  
  Princeton University
  
  Estados Unidos
2. [2] University of Texas at Dallas
  
  University of Texas at Dallas
  
  Estados Unidos
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº Extra 7, 2022 (Ejemplar dedicado a: Special issue in honor of Antonio Córdoba and José Luis Fernández), págs. 2153-2184
Idioma: inglés
DOI: 10.4171/RMI/1390
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Resumen
- 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