On the first eigenvalue of the laplacian on compact surfaces of genus three Ros Mulero, Antonio For any compact Riemannian surface of genus three (Σ,ds2) Yang and Yau proved that the product of the first eigenvalue of the Laplacian λ1(ds2) and the area Area(ds2) is bounded above by 24π. In this paper we improve the result and we show that λ1(ds2)Area(ds2)≤16(4−√7)π≈21.668π. About the sharpness of the bound, for the hyperbolic Klein quartic surface numerical computations give the value ≈21.414π. 2022-09-08T09:59:19Z 2022-09-08T09:59:19Z 2021 info:eu-repo/semantics/article Published version: J. Math. Soc. Japan 74(3): 813-828 (July, 2022). [DOI: 10.2969/jmsj/85898589] http://hdl.handle.net/10481/76582 10.2969/jmsj/85898589 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess Attribution-NonCommercial-NoDerivatives 4.0 Internacional