THE WEIL-PETERSSON GEOMETRY OF THE MODULI SPACE OF RIEMANN SURFACES
THE WEIL-PETERSSON GEOMETRY OF THE MODULI SPACE OF RIEMANN SURFACES
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黎曼曲面模空间的Weil-Peterson几何
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
L. Teo
中科院分区：
文献类型：
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作者：
L. Teo
2007年，Z. Huang证明了在亏格为g的紧致Riemann曲面的模空间M g的厚部分中，Weil-Petersson度量的截面曲率由依赖于内射半径的常数限制，但与亏格g无关。在这篇文章中，我们用另一种方法证明了这个结果。我们还证明了同样的结果也适用于Ricci曲率。对于具有由Weil-Petersson度量诱导的Hilbert结构的泛Teichmuller空间，我们证明了它的截面曲率下有界于一个泛常数.
In 2007, Z. Huang showed that in the thick part of the moduli space M g of compact Riemann surfaces of genus g, the sectional curvature of the Weil-Petersson metric is bounded below by a constant depending on the injectivity radius, but independent of the genus g. In this article, we prove this result by a different method. We also show that the same result holds for Ricci curvature. For the universal Teichmuller space equipped with a Hilbert structure induced by the Weil-Petersson metric, we prove that its sectional curvature is bounded below by a universal constant.