On the first eigenvalue of the laplacian on compact surfaces of genus three
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Ros Mulero, AntonioDate
2021Referencia bibliográfica
Published version: J. Math. Soc. Japan 74(3): 813-828 (July, 2022). [DOI: 10.2969/jmsj/85898589]
Sponsorship
MINECO/FEDER grants no. MTM2017-89677-P; Junta Andalucía grants no. P06-FQM-01642 and P18-FR-4049Abstract
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.