Logarithmic improvements in $$L^{p}$$ L p bounds for eigenfunctions at the critical exponent in the presence of nonpositive curvature
Logarithmic improvements in $$L^{p}$$ L p bounds for eigenfunctions at the critical exponent in the presence of nonpositive curvature
复制标题
在存在非正曲率的情况下，临界指数处的特征函数 $$L^{p}$$ L p 界限的对数改进
DOI：
10.1007/s00222-019-00873-6
复制
发表时间：
2019
影响因子：
3.1
通讯作者：
Sogge, Christopher D.
中科院分区：
文献类型：
--
作者：
Blair, Matthew D.;Sogge, Christopher D.
我们考虑的问题provingbounds的特征函数的Laplacian在高频极限的存在下，非正曲率，更一般地说，流形没有共轭点。特别是，我们证明了在“临界指数”，其中相空间浓度谱的情况下，必须排除估计。我们的工作建立了一个增益的对数的频率在相对于第二作者的classicalbounds的范围内的倒数幂。
We consider the problem of provingbounds for eigenfunctions of the Laplacian in the high frequency limit in the presence of nonpositive curvature and more generally, manifolds without conjugate points. In particular, we prove estimates at the “critical exponent”, where a spectrum of scenarios for phase space concentration must be ruled out. Our work establishes a gain of an inverse power of the logarithm of the frequency in the bounds relative to the classicalbounds of the second author.