Non-existence of Yamabe Minimizers on Singular Spheres
Non-existence of Yamabe Minimizers on Singular Spheres
复制标题
DOI：
10.1007/s12220-022-00923-1
复制
发表时间：
2019-09
期刊：
影响因子：
--
通讯作者：
K. Akutagawa;Ilaria Mondello
中科院分区：
文献类型：
--
作者：
K. Akutagawa;Ilaria Mondello
我们证明，对于尺寸球体，沿着余维二的大圆，赋予锥角大于或等于的标准边锥球面度量，不存在 Yamabe 泛函的极小值。当沿着奇点的锥角小于 时，相应的度量被称为 Yamabe 度量，并且我们表明，其共形类中的所有 Yamabe 度量都是通过保留奇异集的常倍数和共形微分同胚从中获得的。
We prove that a minimizer of the Yamabe functional does not exist for a sphereof dimension, endowed with a standard edge-cone spherical metric of cone angle greater than or equal to, along a great circle of codimension two. When the cone angle along the singularity is smaller than, the corresponding metric is known to be a Yamabe metric, and we show that all Yamabe metrics in its conformal class are obtained from it by constant multiples and conformal diffeomorphisms preserving the singular set.