无需偶性假设的渐近双曲曲面上的预解估计

中文摘要 AI 辅助

我们证明了非紧黎曼流形上拉普拉斯算子的尖锐截断预解估计，这些流形的末端满足Cardoso--Vodev假设，且其在俘获集附近的几何与具有相应预解估计的偶渐近双曲流形一致。作为应用，我们在负曲率渐近双曲曲面上证明了全局Strichartz估计和谱投影估计，无需假设无穷远处的偶性。

英文摘要

We prove a sharp cut-off resolvent estimate for the Laplacian on non-compact Riemannian manifolds whose ends satisfy the Cardoso--Vodev assumption and whose geometry near the trapped set agrees with that of an even asymptotically hyperbolic manifold with the corresponding resolvent estimate. As applications, we show the global Strichartz and spectral projection estimates on negatively curved asymptotically hyperbolic surfaces, without assuming the evenness at infinity.

发表机构

• Mathematical Institute, Rheinische Friedrich-Wilhelms-Universität Bonn（波恩大学数学研究所）

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