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First eigenvalues of geometric operators under the Ricci flow
Authors:Xiaodong Cao
Affiliation:Department of Mathematics, Cornell University, Ithaca, New York 14853-4201
Abstract:In this paper, we prove that the first eigenvalues of $ -Delta + cR$ ( $ cgeq frac14$) are nondecreasing under the Ricci flow. We also prove the monotonicity under the normalized Ricci flow for the cases $ c= 1/4$ and $ rle 0$.

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