On the prescribed scalar curvature problem in RN, local uniqueness and periodicity
On the prescribed scalar curvature problem in RN, local uniqueness and periodicity
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DOI：
10.1016/j.matpur.2015.07.003
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发表时间：
2015-12
期刊：
影响因子：
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通讯作者：
Yinbin Deng;Changshou Lin;Shusen Yan
中科院分区：
文献类型：
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作者：
Yinbin Deng;Changshou Lin;Shusen Yan
我们得到了RN中给定数量曲率问题的冒泡解的局部唯一性结果。这样的结果意味着某些冒泡解保持了标量曲率K（y）的对称性。特别地，本文证明了：如果K（y）在y1中周期，周期为1，且在0处有局部极大值，则爆破集为{（jL，0，n，0）：j= 0，±1，±2，n}的冒泡解在正整数L足够大的条件下，必在y1中周期.
We obtain a local uniqueness result for bubbling solutions of the prescribed scalar curvature problem in R N. Such a result implies that some bubbling solutions preserve the symmetry from the scalar curvature K (y). In particular, we prove in this paper that if K (y) is periodic in y 1 with period 1 and has a local maximum at 0, then a bubbling solution whose blow-up set is {(j L, 0,⋯, 0): j= 0,±1,±2,⋯} must be periodic in y 1 provided the positive integer L is large enough.