Non-compactness of the prescribed Q-curvature problem in large dimensions
Non-compactness of the prescribed Q-curvature problem in large dimensions
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DOI：
10.1007/s00526-011-0477-9
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发表时间：
2009-03
影响因子：
2.1
通讯作者：
Juncheng Wei;Chunyi Zhao
中科院分区：
文献类型：
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作者：
Juncheng Wei;Chunyi Zhao
设（M,g）是一个n≥5维的紧黎曼流形，其曲率为qgbe。规定曲率问题是关于求保形g类中常曲率度规的问题。这就等于找到一个正解来解释为什么p是Paneitz算子。我们证明了对于尺寸sn≥25，规定的q曲率问题的所有正解的集合是非紧的。
Let (M,g) be a compact Riemannian manifold of dimensionN≥ 5 andQgbe itsQcurvature. The prescribedQcurvature problem is concerned with finding metric of constantQcurvature in the conformal class ofg. This amounts to finding a positive solution towherePgis the Paneitz operator. We show that for dimensionsN≥ 25, the set of all positive solutions to the prescribedQcurvature problem isnon-compact.