局部共形平坦黎曼流形上特征值的一些估计

摘要

利用黎曼几何的热核性质和局部共形平坦黎曼流形上的Sobolev不等式,得到了局部共形平坦黎曼流形上高阶特征值的一个估计。并且通过相关特征值不等式给出了局部共形平坦黎曼流形上Schrödinger算子的特征值的个数的一个上界估计。Using the thermal kernel property of Riemann geometry and the Sobolev inequality on a locally conformally flat Riemannian manifold, we obtained an estimate for high-order eigenvalues on such a manifold. And using the correlated eigenvalue gives an upper bound of the number of eigenvalues of Schrödinger operators on a locally conformally flat Riemannian manifold.