First eigenvalue monotonicity for the p-Laplace operator under the Ricci flow
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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)].
KeywordsRicci flow first eigenvalue p-Laplace operator monotonicity
MR(2000) Subject Classification58C40 53C44
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