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Sharp spectral gap for the Finsler p-Laplacian

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Abstract

In this paper, we give a sharp lower bound for the first (nonzero) p-eigenvalue on a compact Finsler manifold M without boundary or with convex boundary if the weighted Ricci curvature RicciN is bounded from below by a constant K in terms of the diameter d of a manifold, dimension, K, p and N. In particular, if RicciN is non-negative, then the first p-eigenvalue is bounded from below by \((p - 1){({\textstyle{{{\pi _p}} \over d}})^p}\), and the equality holds if and only if M is either a circle or a segment.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11671352) and Zhejiang Provincial National Science Foundation of China (Grant No. LY19A010021). The author expresses her sincere thanks to Professor Yibing Shen for his constant encouragement and support. The author also thanks the anonymous referees for their helpful comments, which have improved the presentations of the article and made it more readable.

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  1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    Qiaoling Xia

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  1. Qiaoling Xia
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Xia, Q. Sharp spectral gap for the Finsler p-Laplacian. Sci. China Math. 62, 1615–1644 (2019). https://doi.org/10.1007/s11425-018-9510-5

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  • DOI: https://doi.org/10.1007/s11425-018-9510-5

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