Differential and Integral Equations

Asymptotically hyperbolic manifolds with polyhomogeneous metric

Leonardo Marazzi

Abstract

We analyze the resolvent and define the scattering matrix for asymptotically hyperbolic manifolds with metrics which have a polyhomogeneous expansion near the boundary. We prove that there is always an essential singularity of the resolvent in this setting. We use this analysis to prove an inverse result for conformally compact odd-dimensional Einstein manifolds.

Article information

Source
Differential Integral Equations, Volume 24, Number 9/10 (2011), 973-1000.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012896

Mathematical Reviews number (MathSciNet)
MR2850349

Zentralblatt MATH identifier
1249.58013

Subjects
Primary: 58J50; 35R30 58J50; 35R30

Citation

Marazzi, Leonardo. Asymptotically hyperbolic manifolds with polyhomogeneous metric. Differential Integral Equations 24 (2011), no. 9/10, 973--1000. https://projecteuclid.org/euclid.die/1356012896