We show that the spherical equilateral triangle of diameter \(\frac{\pi }{2}\) is a strict local minimizer of the fundamental gap on the space of the spherical triangles with diameter \(\frac{\pi }{2}\), which partially extends Lu-Rowlett’s result–(Commun Math Phys 319(1): 111–145, 2013) from the plane to the sphere.

中文翻译：

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球面三角形的基本间隙

我们证明了直径为\(\frac{\pi }{2}\)的球面等边三角形是直径为\(\frac{\pi }{2 }\)，它部分地将 Lu-Rowlett 的结果（Commun Math Phys 319(1): 111–145, 2013）从平面扩展到球体。