# Weakly asymptotically hyperbolic manifolds

COMMUNICATIONS IN ANALYSIS AND GEOMETRY（2018）

Abstract

We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to -1 and are C-0, but are not necessarily C-1, conformally compact. We subsequently investigate the rate at which curvature invariants decay at infinity, identifying a conformally invariant tensor which serves as an obstruction to "higher order decay" of the Riemann curvature operator. Finally, we establish Fredholm results for geometric elliptic operators, extending the work of Rafe Mazzeo [21] and John M. Lee [18] to this setting. As an application, we show that any weakly asymptotically hyperbolic metric is conformally related to a weakly asymptotically hyperbolic metric of constant negative scalar curvature.

MoreTranslated text

Key words

weakly

AI Read Science

Must-Reading Tree

Example

Generate MRT to find the research sequence of this paper

Chat Paper

Summary is being generated by the instructions you defined