Sub-Laplacian eigenvalue bounds on sub-Riemannian manifolds
Sub-Laplacian eigenvalue bounds on sub-Riemannian manifolds
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DOI：
10.2422/2036-2145.201409_005
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发表时间：
2014-07
影响因子：
1.4
通讯作者：
Asma Hassannezhad;G. Kokarev
中科院分区：
文献类型：
--
作者：
Asma Hassannezhad;G. Kokarev
研究了正则次黎曼流形上固有次拉普拉斯算子的特征值问题。证明了共形次黎曼度量的次拉普拉斯特征值λk的上界是渐近尖锐的，即k→+∞。对于具有较低Ricci曲率界的Sasakian流形，以及更一般地，对于与这类Sasakian流形共形的接触度量流形，我们得到了特征值不等式，这些特征值不等式可以看作是Korvaar和Buser在黎曼几何中经典结果的版本。
We study eigenvalue problems for intrinsic sub-Laplacians on regular sub-Riemannian manifolds. We prove upper bounds for sub-Laplacian eigenvalues λk of conformal sub-Riemannian metrics that are asymptotically sharp as k→+∞. For Sasakian manifolds with a lower Ricci curvature bound, and more generally, for contact metric manifolds conformal to such Sasakian manifolds, we obtain eigenvalue inequalities that can be viewed as versions of the classical results by Korevaar and Buser in Riemannian geometry.