| 吴加勇.Yamabe流上的Laplace算子的第一特征值[J].数学年刊A辑,2009,30(5):631~638 |
| Yamabe流上的Laplace算子的第一特征值 |
| The First Eigenvalue of the Laplace Operator Under the Yamabe Flow |
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| DOI： |
| 中文关键词: 特征值单调性 Yamabe流 渐近行为 |
| 英文关键词:Eigenvalue monotonicity, Yamabe flow, Asymptotic behavior |
| 基金项目:家自然科学基金(No.10871069)资助的项目 |
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| 中文摘要: |
| 首先建立了在Yamabe流上的Laplace算子的第一特征值的演化公式.作为其应用,在非规范化的Yamabe流上,得到了关于第一特征值的一些有趣的单调量(不减或不增).然后,研究了在规范化的Yamabe流上的第一特征值的渐近行为,并且给出了第一特征值的渐近上界的一个直接证明. |
| 英文摘要: |
| In this note, on one hand the author establishes the evolution formulas for the
first eigenvalue of the Laplace operator under the Yamabe flow. As applications, one can
find some new interesting monotonic quantities, involving the first eigenvalue of the Laplace
operator, which are monotonic (non-decreasing or non-increasing) under the unnormalized
Yamabe flow. On the other hand, the author studies the asymptotic behavior of the first
eigenvalue under the normalized Yamabe flow and gives a direct short proof for an asymptotic
upper limit estimate. |
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