2012/07/25 by Jean-Marc Bouclet, Jean‐Marc Bouclet, Bouclet, Jean-Marc
Engineering · Mathematics · #53B20 #58J60 #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Stability and Controllability of Differential Equations #math.DG #msc:53B20 #msc:58J60
paper · pdf · doi:10.48550/arxiv.1207.5940
Corrected typos. Will appear in Osaka journal of mathematics
openalex publication_date 2012/07/25 · arxiv created 2013/04/20 · arxiv updated 2013/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In many problems of PDE involving the Laplace-Beltrami operator on manifolds with ends, it is often useful to introduce radial or geodesic normal coordinates near infinity. In this paper, we prove the existence of such coordinates for a general class of manifolds with ends, which contains asymptotically conical and hyperbolic manifolds. We study the decay rate to the metric at infinity associated to radial coordinates and also show that the latter metric is always conformally equivalent to the metric at infinity associated to the original coordinate system. We finally give several examples illustrating the sharpness of our results.