典型几何上Ricci流下的特征值

侯松波

数学学报 ›› 2017, Vol. 60 ›› Issue (4) : 583-594.

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数学学报 ›› 2017, Vol. 60 ›› Issue (4) : 583-594. DOI: 10.12386/A2017sxxb0048
论文

典型几何上Ricci流下的特征值

    侯松波
作者信息 +

Eigenvalues Under the Ricci Flow of Model Geometries

    Song Bo HOU
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摘要

研究了典型几何上规范Ricci流下Laplace——Beltrami算子第一特征值的发展行为.在每一个Bianchi类中,我们估计了特征值的导数.构造了Ricci流下的单调量并得到了特征值的上下界估计.

Abstract

We study the evolving behaviors of the first eigenvalue of the Laplace-Beltrami operator under the normalized Ricci flow of model geometries.In every Bianchi class,we estimate the derivative of the eigenvalue.Then we construct monotonic quantities under the Ricci flow and obtain upper and lower bounds for the eigenvalue.

关键词

局部齐性3维流形 / Ricci流 / 特征值 / 估计

Key words

locally homogeneous 3-manifold / Ricci flow / eigenvalue / estimate

引用本文

导出引用
侯松波. 典型几何上Ricci流下的特征值. 数学学报, 2017, 60(4): 583-594 https://doi.org/10.12386/A2017sxxb0048
Song Bo HOU. Eigenvalues Under the Ricci Flow of Model Geometries. Acta Mathematica Sinica, Chinese Series, 2017, 60(4): 583-594 https://doi.org/10.12386/A2017sxxb0048

参考文献

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基金

国家自然科学基金资助项目(11001268);中国高校科学基金资助项目(2014QJ002)

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