Complete manifolds with bounded curvature and spectral gaps
Complete manifolds with bounded curvature and spectral gaps
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具有有界曲率和谱间隙的完整流形
DOI：
10.1016/j.jde.2016.05.002
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Hung Tran
中科院分区：
文献类型：
--
作者：
R. Schoen;Hung Tran
研究了具有有界曲率和正内射半径的完备非紧流形的谱。我们给出了一般的条件，这意味着他们的本质谱有一个任意大的有限数量的差距。特别地，对于紧致流形的任何非紧覆盖，在基上存在一个度量，使得提升的度量在其本质谱中有任意大的有限个间隙。此外，对于任何完备非紧流形有界曲率和正内射半径，我们构造了一个度量一致等价于给定的（也有界曲率和正内射半径），其本质谱中有任意大的有限个间隙。
We study the spectrum of complete noncompact manifolds with bounded curvature and positive injectivity radius. We give general conditions which imply that their essential spectrum has an arbitrarily large finite number of gaps. In particular, for any noncompact covering of a compact manifold, there is a metric on the base so that the lifted metric has an arbitrarily large finite number of gaps in its essential spectrum. Also, for any complete noncompact manifold with bounded curvature and positive injectivity radius we construct a metric uniformly equivalent to the given one (also of bounded curvature and positive injectivity radius) with an arbitrarily large finite number of gaps in its essential spectrum.