Selberg's 1/4 conjecture motivated the question of existence of finite area hyperbolic surfaces with first non-zero eigenvalue of the Laplacian at least 1/4. We shall address this question for closed hyperbolic surfaces and show that it has a positive answer in the case of genus two.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/3050