For the Laplace operator with Dirichlet boundary conditions on convex domains in \(\mathbb H^n\), \(n\ge 2\), we prove that the product of the fundamental gap with the square of the diameter can be arbitrarily small for domains of any diameter.

中文翻译：

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$$\mathbb {H}^n$$ H n 中凸域基本间隙的消失

对于\(\mathbb H^n\) , \(n\ge 2\) 中凸域上具有狄利克雷边界条件的拉普拉斯算子，我们证明了基本间隙与直径平方的乘积可以任意小适用于任何直径的域。