2008/09/04 by Daniel Grieser, Grieser, Daniel, Eugenie Hunsicker +2 · 1 citation
Mathematics · #58J40 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.AP #math.DG #msc:58J40
paper · pdf · doi:10.48550/arxiv.0809.0925
44 pages, 2 figures -- Some explanations, references added; changed normalization of index sets in full calculus to make it more natural; made full calculus composition result more complete
openalex publication_date 2008/09/04 · arxiv created 2009/09/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is the first of two papers constructing a calculus of pseudodifferential operators suitable for doing analysis on Q-rank 1 locally symmetric spaces and Riemannian manifolds generalizing these. This generalization is the interior of a manifold with boundary, where the boundary has the structure of a tower of fibre bundles. The class of operators we consider on such a space includes those arising naturally from metrics which degenerate to various orders at the boundary, in directions given by the tower of fibrations. As well as Q-rank 1 locally symmetric spaces, examples include Ricci-flat metrics on the complement of a divisor in a smooth variety constructed by Tian and Yau. In this first part of the calculus construction, parametrices are found for "fully elliptic differential \bfa-operators", which are uniformly elliptic operators on these manifolds that satisfy an additional invertibility condition at infinity. In the second part we will consider operators that do not satisfy this condition.