Eigenvalue estimates for the drifting Laplacian and the p-Laplacian on submanifolds of warped products
Eigenvalue estimates for the drifting Laplacian and the p-Laplacian on submanifolds of warped products
复制标题
翘曲产品子流形上的漂移拉普拉斯算子和 p-拉普拉斯算子的特征值估计
DOI：
10.1080/00036811.2019.1679793
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发表时间：
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影响因子：
1.1
通讯作者：
Zeng Ling-Zhong
中科院分区：
文献类型：
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作者：
Lu Wei;Mao Jing;Wu Chuan-Xi;Zeng Ling-Zhong
本文研究了浸入型翘曲积的极小子流形M，其中为正，并且给出了M中开域上p-Laplacian的第一特征值，即漂移Laplacian的加权基音的下界。这一结果使我们能够处理以圆柱、圆锥、球面和伪双曲空间为界的极小子流形的谱估计，同时也得到了一些有趣的副产品。例如，我们可以证明欧氏m-空间（）中任何圆柱有界极小超曲面的基调是正的。
ABSTRACT In this paper, we investigate minimal submanifolds M immersed into warped products of type , where is positive, and can give lower bounds for the weighted fundamental tone of the drifting Laplacian, the first eigenvalue of the p-Laplacian on open domains in M. This achievement enables us to deal with spectral estimates for minimal submanifolds bounded by cylinders, cones, spheres and pseudo-hyperbolic spaces, and meanwhile some interesting byproducts can be obtained. For instance, we can show that the fundamental tone of any cylindrically bounded minimal hypersurface in the Euclidean m-space ( ) is positive.