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Noncompact complete Riemannian manifolds with singular continuous spectrum embedded into the essential spectrum of the Laplacian, I. The hyperbolic case
Transactions of the American Mathematical Society ( IF 1.3 ) Pub Date : 2020-05-26 , DOI: 10.1090/tran/8112 Svetlana Jitomirskaya , Wencai Liu
Transactions of the American Mathematical Society ( IF 1.3 ) Pub Date : 2020-05-26 , DOI: 10.1090/tran/8112 Svetlana Jitomirskaya , Wencai Liu
We construct Riemannian manifolds with singular continuous spectrum embedded in the absolutely continuous spectrum of the Laplacian. Our manifolds are asymptotically hyperbolic with sharp curvature bounds.
中文翻译:
具有奇异连续谱的非紧致完整黎曼流形嵌入拉普拉斯算子的本质谱中,I. 双曲线情况
我们用嵌入拉普拉斯算子的绝对连续谱中的奇异连续谱构造黎曼流形。我们的流形是渐近双曲线的,具有尖锐的曲率边界。
更新日期:2020-05-26
中文翻译:
具有奇异连续谱的非紧致完整黎曼流形嵌入拉普拉斯算子的本质谱中,I. 双曲线情况
我们用嵌入拉普拉斯算子的绝对连续谱中的奇异连续谱构造黎曼流形。我们的流形是渐近双曲线的,具有尖锐的曲率边界。