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<p>Under the assumption of integral <i>m</i>-Bakry–Émery Ricci curvature, we give an Escobar–Lichnerowicz–Reilly type eigenvalue estimate for the weighted <i>p</i>-Laplacian on compact smooth metric measure spaces with or without boundaries. This conclusion is a generalization and improvement of Wang–Li’s result in the case of integral Bakry–Émery Ricci curvature, and of Seto–Wei’s one to the compact metric measure space setting. Our main tools are the weighted <i>p</i>-Bochner formula and the weighted <i>p</i>-Reilly formula.</p>

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Escobar–Lichnerowicz–Reilly Type Eigenvalue Estimate for the Weighted p-Laplacian on Manifolds with Integral Ricci Curvature

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Yongtao Liu

摘要

Under the assumption of integral m-Bakry–Émery Ricci curvature, we give an Escobar–Lichnerowicz–Reilly type eigenvalue estimate for the weighted p-Laplacian on compact smooth metric measure spaces with or without boundaries. This conclusion is a generalization and improvement of Wang–Li’s result in the case of integral Bakry–Émery Ricci curvature, and of Seto–Wei’s one to the compact metric measure space setting. Our main tools are the weighted p-Bochner formula and the weighted p-Reilly formula.