最短闭测地线长度的Calabi-Croke球面的局部极值
Local extremality of the Calabi-Croke sphere for the length of the shortest closed geodesic
摘要：
最近，F. Balacheff证明了由两个平面1单位边等边三角形沿其边界胶合而成的Calabi-Croke球面是具有固定面积圆锥奇点的黎曼球面中最短闭测地线长度的局部极值。我们给出了这个定理的另一种证明，它不使用单值化定理，并将结果推广到Finsler度量。
英文摘要：
Recently, F. Balacheff proved that the Calabi-Croke sphere made of two flat 1-unit-side equilateral triangles glued along their boundaries is a local extremum for the length of the shortest closed geodesic among the Riemannian spheres with conical singularities of fixed area. We give an alternative proof of this theorem, which does not make use of the uniformization theorem, and extend the result to Finsler metrics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
