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    • Eigenvalue estimates for submanifolds with bounded $f$ -mean curvature

      GUANGYUE HUANG BINGQING MA

      Research Article Volume 127 Issue 2 April 2017 pp 375-381

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/127/02/0375-0381

    • Keywords

       

      Eigenvalue estimates; submanifolds; weighted manifolds; $f$ -mean curvature

    • Abstract

       

      In this paper, we obtain an extrinsic low bound to the first non-zero eigenvalue of the $f$ -Laplacian on complete noncompact submanifolds of the weighted Riemannian manifold ($H^{m}(−1), e^{−f} dv$) with respect to the f -mean curvature. In particular, our results generalize those of Cheung and Leung in $\it{Math}. \bf{Z. 236}$ (2001) 525–530.

    • Author Affiliations

       

      GUANGYUE HUANG1 2 BINGQING MA1 2

      1. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, People’s Republic of China
      2. Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Xinxiang 453007, People’s Republic of China

    • Dates

       
      Published
      20 April 2017
      Manuscript received
      17 March 2015
      Manuscript revised
      3 June 2016
      Accepted
      7 June 2016
      Early published
      Unedited version published online
      Final version published online
      15 April 2017

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