Inequalities for eigenvalues of elliptic operators in divergence form on Riemannian manifolds
Inequalities for eigenvalues of elliptic operators in divergence form on Riemannian manifolds
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DOI：
10.1007/s10231-010-0129-2
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发表时间：
2010-02
影响因子：
1
通讯作者：
M. Carmo;Qiaoling Wang;C. Xia
中科院分区：
文献类型：
--
作者：
M. Carmo;Qiaoling Wang;C. Xia
本文研究了具有边界（可能为空）的紧致黎曼流形上散度型椭圆算子的特征值，得到了一个一般不等式。利用这个不等式，我们证明了欧氏空间中完备子流形的紧致域上的散度型椭圆算子的特征值的普遍不等式，以及包含特殊函数的完备流形的特征值的普遍不等式，这些特殊函数包括Ricci曲率有界的Hadamard流形，一类翘曲积流形，欧氏空间与任意完备流形的乘积，以及包含球面特征映射的流形.
In this paper, we study eigenvalues of elliptic operators in divergence form on compact Riemannian manifolds with boundary (possibly empty) and obtain a general inequality for them. By using this inequality, we prove universal inequalities for eigenvalues of elliptic operators in divergence form on compact domains of complete submanifolds in a Euclidean space, and of complete manifolds admitting special functions which include the Hadamard manifolds with Ricci curvature bounded below, a class of warped product manifolds, the product of Euclidean spaces with any complete manifold and manifolds admitting eigenmaps to a sphere.