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Eigenvalue comparisons in Steklov eigenvalue problem and some other eigenvalue estimates

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 23 Sep 2019Embargo end date: 01 Jan 2018 English Publisher:Springer Science and Business Media LLCJournal:Revista Matemática Complutense, volume 33, pages 389-414 (issn: 1139-1138, eissn: 1988-2807,

Authors: Feng Du; Chuanxi Wu; Yan Zhao; Jing Mao; Jing Mao;

doi: 10.1007/s13163-019-00322-1 , 10.48550/arxiv.1810.08281

arXiv: http://arxiv.org/abs/1810.08281

Eigenvalue comparisons in Steklov eigenvalue problem and some other eigenvalue estimates

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Abstract

In this paper, two interesting eigenvalue comparison theorems for the first non-zero Steklov eigenvalue of the Laplacian have been established for manifolds with radial sectional curvature bounded from above. Besides, sharper bounds for the first non-zero eigenvalue of the Wentzell eigenvalue problem of the weighted Laplacian, which can be seen as a natural generalization of the classical Steklov eigenvalue problem, have been obtained.

Comments are welcome. 24 pages. A revised version will appear in Revista Matem\'{a}tica Complutense

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Keywords

Mathematics - Differential Geometry, Differential Geometry (math.DG), FOS: Mathematics, 35P15, 53C20

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