# Yue Gao's research while affiliated with Peking University and other places

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## Publications (3)

We obtain the exact values of the systoles of these hyperbolic surfaces of genus g with cyclic symmetry of the maximum order and the next maximum order. Precisely, for the genus g hyperbolic surface with order 4g + 2 cyclic symmetry, the systole is \(\left( {1 + \cos {{\rm{\pi }} \over {2g + 1}} + \cos {{2{\rm{\pi }}} \over {2g + 1}}} \right)\) whe...

We give the formula for the maximal systole of the surface admits the largest $S^3$-extendable abelian group symmetry. The result we get is $2\mathrm{arccosh} K$. Here \begin{eqnarray*} K &=& \sqrt[3]{\frac{1}{216}L^3 +\frac{1}{8} L^2 + \frac{5}{8} L - \frac{1}{8} + \sqrt{\frac{1}{108}L(L^2+18L+27)} } & & + \sqrt[3]{\frac{1}{216}L^3 +\frac{1}{8} L^...

We obtain the exact values of the systoles of these hyperbolic surfaces of genus $g$ with cyclic sysmetries of the maximum order and the next maximum order. Precisely: for genus $g$ hyperbolic surface with order $4g+2$ cyclic symmetry, the systole is $2\mathrm{arccosh} (1+\cos \frac{\pi}{2g+1}+\cos \frac{2\pi}{2g+1})$ when $g\ge 7$, and for genus $...

## Citations

... The same result was also recently obtained by Bai et al. [6]. Our proof gives more insight into the representation in D g of closed geodesics on M g . ...