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Estimate and monotonicity of the first eigenvalue under the Ricci flow |
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| Authors: | |
| Institution: | 1.Department of Mathematics,Cornell University,Ithaca,USA;2.Department of Applied Mathematics, College of Science, East Campus,China Agricultural University,Beijing,People’s Republic of China;3.Department of Mathematics,Utah Valley University,Orem,USA |
| Abstract: | In this paper, we first derive a monotonicity formula for the first eigenvalue of on a closed surface with nonnegative scalar curvature under the (unnormalized) Ricci flow. We then derive a general evolution formula for the first eigenvalue under the normalized Ricci flow. As an application, we obtain various monotonicity formulae and estimates for the first eigenvalue on closed surfaces. |
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