论文标题
球形三角形的根本差距
Fundamental gaps of spherical triangles
论文作者
论文摘要
我们针对球形月球和球形三角形明确计算了Dirichlet征值和特征，这些函数是LUNES的一半，并表明当Lune的角度为零时，基本差距会变为无穷大。然后，我们显示了直径的球形等边三角形$ \fracπ{2} $是严格的局部最小化距离的基本差距，这是球形三角形的直径$ \fracπ{2} $的局部差距，这部分扩展了Lu-Rowlett从飞机上延伸到圆形的。
We compute Dirichlet eigenvalues and eigenfunctions explicitly for spherical lunes and the spherical triangles which are half the lunes, and show that the fundamental gap goes to infinity when the angle of the lune goes to zero. Then we show the spherical equilateral triangle of diameter $\fracπ{2}$ is a strict local minimizer of the fundamental gap on the space of the spherical triangles with diameter $\fracπ{2}$, which partially extends Lu-Rowlett's result from the plane to the sphere.
