May 2020
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35 Reads
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2 Citations
Science China Mathematics
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 when g ⩾ 7, and for the genus g hyperbolic surface with order 4g cyclic symmetry, the systole is when g ⩾ 4.