Abstract

Motivated by an example of Shih [10], we compute the fundamental gap of a family of convex domains in the hyperbolic plane H2, showing that for some of them (Formula Presented), where D is the diameter of the domain and ��1, ��2 are the first and second Dirichlet eigenvalues of the Laplace operator on the domain. The result contrasts with what is known in Rn or Sn, where (Formula Presented) for convex domains [1, 5, 7, 9]. We also show that the fundamental gap of the example in Shih���s article is still greater than (Formula Presented) , even though the first eigenfunction of the Laplace operator is not logconcave.