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arXiv 2103.09997math.DGmath.GT
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$\mathbb{H}^{2}\times\mathbb{H}^{2}\times\mathbb{H}^{2}$覆盖的闭流形的单形体积的下界

Lower Bound for the Simplicial Volume of Closed Manifolds Covered by $\mathbb{H}^{2}\times\mathbb{H}^{2}\times\mathbb{H}^{2}$

Xiaofeng Meng

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摘要：

我们估计的$\ell^{\infty}$ -范数的体积形式$\mathbb{H}^2\times\mathbb{H}^2\times\mathbb{H}^2$视为一类在$H_{c}^{6}(\mathrm{PSL}_{2}\mathbb{R}\times\mathrm{PSL}_{2}\mathbb{R}\times\mathrm{PSL}_{2}\mathbb{R};\mathbb{R})$。这给出了由$\mathbb{H}^{2}\times\mathbb{H}^{2}\times\mathbb{H}^{2}$覆盖的闭黎曼流形的单纯体积的下界。这些事实的证明产生一个算法来计算由$\big(\mathbb{H}^2\big)^n$覆盖的闭黎曼流形的下界。

英文摘要：

We estimate the upper bound for the $\ell^{\infty}$-norm of the volume form on $\mathbb{H}^2\times\mathbb{H}^2\times\mathbb{H}^2$ seen as a class in $H_{c}^{6}(\mathrm{PSL}_{2}\mathbb{R}\times\mathrm{PSL}_{2}\mathbb{R}\times\mathrm{PSL}_{2}\mathbb{R};\mathbb{R})$. This gives the lower bound for the simplicial volume of closed Riemennian manifolds covered by $\mathbb{H}^{2}\times\mathbb{H}^{2}\times\mathbb{H}^{2}$. The proof of these facts yields an algorithm to compute the lower bound of closed Riemannian manifolds covered by $\big(\mathbb{H}^2\big)^n$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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