We introduce a class of "weakly asymptotically hyperbolic" geometries whosesectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$,conformally compact. We subsequently investigate the rate at which curvatureinvariants decay at infinity, identifying a conformally invariant tensor whichserves as an obstruction to "higher order decay" of the Riemann curvatureoperator. Finally, we establish Fredholm results for geometric ellipticoperators, extending the work of Rafe Mazzeo and John M. Lee to this setting.As an application, we show that any weakly asymptotically hyperbolic metric isconformally related to a weakly asymptotically hyperbolic metric of constantnegative curvature.
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机译：我们引入一类“弱渐近双曲”几何形状，其截面曲率趋于$ -1 $且为$ C ^ 0 $，但不一定为$ C ^ 1 $，因此非常紧凑。随后，我们研究了曲率不变性在无穷大处衰减的速率，确定了共形不变的张量，该张量充当了黎曼曲率算子的“高阶衰减”的障碍。最后，我们建立了几何椭圆算子的Fredholm结果，将Rafe Mazzeo和John M.Lee的工作扩展到此设置。
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