Abstract
<p style='text-indent:20px;'>In this paper, we first study the fractional Yamabe solitons, which are the self-similar solutions to fractional Yamabe flow.We prove some rigidity results and Liouville type results for such solitons.We thenconsider the fractional Nirenberg problem:the problem of prescribing fractional order curvature on the sphere.More precisely, we prove that there exists a conformal metric on the unit sphere such that itsfractional order curvature is <inline-formula><tex-math id="M1">\begin{document}$ f $\end{document}</tex-math></inline-formula>, when <inline-formula><tex-math id="M2">\begin{document}$ f $\end{document}</tex-math></inline-formula> possesses certain reflection or rotation symmetry.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Analysis,General Medicine
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