论文标题
在laplacian的第一个特征值上
On the first eigenvalue of the laplacian on compact surfaces of genus three
论文作者
论文摘要
对于任何紧凑的riemannian属属的riemannian表面，三$（σ，ds^2）$ yan和yau证明了laplacian $λ_1（ds^2）$的第一个特征值的乘积和$24π$限制了$24π$。在本文中，我们改进了结果，并表明$λ_1（ds^2）区域（ds^2）\ leq16（4- \ sqrt {7}）π\ your 21.668 \，π$。关于绑定的清晰度，对于双曲线klein四分之一的表面数值计算，可得出$ \ \ \ 21.414 \，π$的值。
For any compact riemannian surface of genus three $(Σ,ds^2)$ Yang and Yau proved that the product of the first eigenvalue of the Laplacian $λ_1(ds^2)$ and the area $Area(ds^2)$ is bounded above by $24π$. In this paper we improve the result and we show that $λ_1(ds^2)Area(ds^2)\leq16(4-\sqrt{7})π\approx 21.668\,π$. About the sharpness of the bound, for the hyperbolic Klein quartic surface numerical computations give the value $\approx 21.414\,π$.
