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Eigenvalue estimates for submanifolds with bounded f-mean curvature

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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−fdv) with respect to the f-mean curvature. In particular, our results generalize those of Cheung and Leung in Math. Z. 236 (2001) 525–530.

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Acknowledgements

The authors would like to thank the referee for some helpful comments which made this paper more readable. The research of the first author is supported by NSFC (Nos 11371018, 11171091, 11671121), Henan Provincial Key Teacher (No. 2013GGJS-057) and IRTSTHN (14IRTSTHN023). The research of the second author is supported by NSFC (No. 11401179) and Henan Provincial Education Department (No. 14B110017).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, People’s Republic of China

    GUANGYUE HUANG & BINGQING MA

  2. Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Xinxiang, 453007, People’s Republic of China

    GUANGYUE HUANG & BINGQING MA

Authors
  1. GUANGYUE HUANG
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  2. BINGQING MA
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Correspondence to BINGQING MA.

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Communicating Editor: Mj Mahan

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HUANG, G., MA, B. Eigenvalue estimates for submanifolds with bounded f-mean curvature. Proc Math Sci 127, 375–381 (2017). https://doi.org/10.1007/s12044-016-0308-1

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  • DOI: https://doi.org/10.1007/s12044-016-0308-1

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