2012/06/23 by András Vasy, Vasy, András
Computer Science · Mathematics · #35L05 #35P25 (Primary) #58J47 (Secondary) #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1206.5454
openalex publication_date 2012/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show the analytic continuation of the resolvent of the Laplacian on\nasymptotically hyperbolic spaces on differential forms, including high energy\nestimates in strips. This is achieved by placing the spectral family of the\nLaplacian within the framework developed, and applied to scalar problems, by\nthe author recently, roughly by extending the problem across the boundary of\nthe compactification of the asymptotically hyperbolic space in a suitable\nmanner. The main novelty is that the non-scalar nature of the operator is dealt\nwith by relating it to a problem on an asymptotically Minkowski space to\nmotivate the choice of the extension across the conformal boundary.\n