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

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Publications (3)


Systoles of hyperbolic surfaces with big cyclic symmetry
  • Article

May 2020

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35 Reads

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2 Citations

Science China Mathematics

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Yue Gao

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Shicheng Wang

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 (1+cosπ2g+1+cos2π2g+1)\left( {1 + \cos {{\rm{\pi }} \over {2g + 1}} + \cos {{2{\rm{\pi }}} \over {2g + 1}}} \right) when g ⩾ 7, and for the genus g hyperbolic surface with order 4g cyclic symmetry, the systole is (1+2cosπ2g)\left( {1 + 2\cos {{\rm{\pi }} \over {2g}}} \right) when g ⩾ 4.


Maximal systole of hyperbolic surface with largest S3S^3 extendable abelian symmetry

November 2019

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15 Reads

We give the formula for the maximal systole of the surface admits the largest S3S^3-extendable abelian group symmetry. The result we get is 2arccoshK2\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^2 + \frac{5}{8} L - \frac{1}{8} - \sqrt{\frac{1}{108}L(L^2+18L+27)} } & & + \frac{L+3}{6}. \end{eqnarray*} and L=4cos2πg1L= 4\cos^2 \frac{\pi}{g-1}.


Figure 14.
Figure 17.
Figure 18.
Figure 27) Now we prove this distance is larger than 2h i by the formulae of the quadrilateral: x is a point moving on the diameter AA between H and O. x is its deck transformation image. x moves as x moves. We calculate inf x∈HO d(x, x ) and compare it with 2h i . In Figure 27, we have obtained |R 1 R 2 | in (5.1). Then in the quadrilateral R 1 R 2 x x, by (3.10),
Figure 33.
Systoles of hyperbolic surfaces with big cyclic symmetry
  • Preprint
  • File available

December 2018

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52 Reads

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 2arccosh(1+cosπ2g+1+cos2π2g+1)2\mathrm{arccosh} (1+\cos \frac{\pi}{2g+1}+\cos \frac{2\pi}{2g+1}) when g7g\ge 7, and for genus g hyperbolic surface with order 4g cyclic symmetry, the systole is 2arccosh(1+2cosπ2g)2\mathrm{arccosh} (1+2\cos \frac{\pi}{2g}) when g4g\ge4.

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Citations (1)


... 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 . ...

Reference:

Delaunay triangulations of generalized Bolza surfaces
Systoles of hyperbolic surfaces with big cyclic symmetry
  • Citing Article
  • May 2020

Science China Mathematics