Abstract
In this note, we discuss the monotonicity of the first eigenvalue of the p-Laplace operator (p ≥ 2) along the Ricci flow on closed Riemannian manifolds. We prove that the first eigenvalue of the p-Laplace operator is nondecreasing along the Ricci flow under some different curvature assumptions, and therefore extend some parts of Ma’s results [Ann. Glob. Anal. Geom., 29, 287–292 (2006)].
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Supported by National Natural Science Foundation of China (Grant No. 10871069)
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Wu, J.Y. First eigenvalue monotonicity for the p-Laplace operator under the Ricci flow. Acta. Math. Sin.-English Ser. 27, 1591–1598 (2011). https://doi.org/10.1007/s10114-011-8565-5
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DOI: https://doi.org/10.1007/s10114-011-8565-5