摘要 : Motivated by an example of Shih [10], we compute the fundamental gap of a family of convex domains in the hyperbolic plane H-2, showing that for some of them lambda(2) - lambda(1) < 3 pi(2)/D-2, where D is the diameter of the doma... 展开 Motivated by an example of Shih [10], we compute the fundamental gap of a family of convex domains in the hyperbolic plane H-2, showing that for some of them lambda(2) - lambda(1) < 3 pi(2)/D-2, where D is the diameter of the domain and lambda(1), lambda(2) are the first and second Dirichlet eigenvalues of the Laplace operator on the domain. The result contrasts with what is known in R-n or S-n, where lambda(2) - lambda(1) < 3 pi(2)/D-2 convex domains [1, 5, 7, 9]. We also show that the fundamental gap of the example in Shih's article is still greater than 3 pi(2)/2D(2) , even though the first eigenfunction of the Laplace operator is not logconcave. 收起