Lower bound estimates for the first eigenvalue of the weighted p-Laplacian on smooth metric measure spaces

Yu-Zhao Wang, Huai-Qian Li

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    Abstract

    New lower bounds of the first nonzero eigenvalue of the weighted p-Laplacian are established on compact smooth metric measure spaces with or without boundaries. Under the assumption of positive lower bound for the m-Bakry-Émery Ricci curvature, the Escobar-Lichnerowicz-Reilly type estimates are proved; under the assumption of nonnegative ∞-Bakry-Émery Ricci curvature and the m-Bakry-Émery Ricci curvature bounded from below by a non-positive constant, the Li-Yau type lower bound estimates are given. The weighted p-Bochner formula and the weighted p-Reilly formula are derived as the key tools for the establishment of the above results.
    Original languageEnglish
    Pages (from-to)23-42
    Number of pages20
    JournalDifferential Geometry and its Applications
    Volume45
    DOIs
    Publication statusPublished - Apr 2016

    Keywords

    • eigenvalue estimate
    • Bakry–Émery Ricci curvature
    • smooth metric measure space
    • weighted p-Bochner formula
    • weighted p-Laplacian
    • weighted p-Reilly formula

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