Pak Tung Ho
Department of Mathematics, Sogang University, Seoul 04107, Korea
Received September 2018 Revised July 2019 Published October 2019
Fund Project: The author is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2019041021)
Using the flow method, we prove an existence result for the problem of prescribing the $ Q $-curvature on the even dimensional sphere $ S^n $. More precisely, we prove that there exists a conformal metric on $ S^n $ such that its $ Q $-curvature is $ f $, when $ f $ possesses certain symmetry.
Keywords: Q-curvature, Nirenberg's problem, geometric flow.
Mathematics Subject Classification: Primary: 53C44, 35K55, 53A30; Secondary: 53C21.
Citation: Pak Tung Ho. Prescribing $ Q $-curvature on $ S^n $ in the presence of symmetry. Communications on Pure & Applied Analysis, 2020, 19 (2) : 715-722. doi: 10.3934/cpaa.2020033
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