Systole and _2g-2 of closed hyperbolic surfaces of genus g
نویسندگان
چکیده
We apply topological methods to study eigenvalues of the Laplacian on closed hyperbolic surfaces. For any closed hyperbolic surface S of genus g , we get a geometric lower bound on 2g 2.S/ W 2g 2.S/ > 1=4C 0.S/ > 0; where 0.S/ is an explicit constant which depends only on the systole of S . Mathematics Subject Classification (2010). Primary 30F; Secondary 35P05, 35P15.
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