In [SWW], S. Seto, L. Wang and G. Wei proved that the gap between the first two Dirichlet eigenvalues of a convex domain in the unit sphere is at least as large as that for an associated operator on an interval with the same diameter, provided that the domain has the diameter at most $\pi/2$. In this paper, we extend Seto-Wang-Wei's result to convex domains in the unit sphere with diameter less than $\pi$.

中文翻译：

---

球体中凸域的基本间隙

在 [SWW] 中，S. Seto、L. Wang 和 G. Wei 证明了单位球面中凸域的前两个 Dirichlet 特征值之间的差距至少与具有相同的直径，前提是该域的直径最多为 $\pi/2$。在本文中，我们将 Seto-Wang-Wei 的结果扩展到单位球体中直径小于 $\pi$ 的凸域。