Lower bound estimates for the first eigenvalue of the weighted p-Laplacian on smooth metric measure spaces |
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Institution: | 1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China;2. School of Mathematics, Sichuan University, Chengdu 610064, China;3. Department of Mathematics, Macquarie University, NSW 2109 Sydney, Australia |
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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. |
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Keywords: | Eigenvalue estimate Bakry–Émery Ricci curvature Smooth metric measure space |
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