Local extremality of the Calabi–Croke sphere for the length of the shortest closed geodesic
Local extremality of the Calabi–Croke sphere for the length of the shortest closed geodesic
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最短闭合测地线长度的卡拉比-克罗克球的局部极值
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
S. Sabourau
中科院分区：
文献类型：
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作者：
S. Sabourau
最近，Balacheff [j]，“二球上的局部最优舒张不等式”。[a] . 2(2010)[109-121]证明了Calabi-Croke球是具有固定面积圆锥奇点的黎曼球中最短封闭测地线长度的局部极值，该球由两个沿其边界粘接的扁平1单位边等边三角形组成。我们给出了这个定理的另一种证明，它不使用均匀化定理，并延续到Lipschitz距离拓扑。进一步，我们将结果推广到Finsler指标。
Recently, Balacheff [‘A local optimal diastolic inequality on the two‐sphere’, J. Topol. Anal. 2 (2010) 109–121] 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 carries over to the Lipschitz distance topology. Furthermore, we extend the result to Finsler metrics.