【摘 要】
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The fractional Yamabe problem, proposed by Gonzalez and Qing in 2013 as a nonlocal analogue of the famous Yamabe problem, is a geometric question which conc
【机 构】
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PontificiaUniversidadCatolicadeChile,Chile
【出 处】
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2016年非线性偏微分方程和变分方法及其应用研讨会(Workshop on Nonlinear PDEs and Cal
论文部分内容阅读
The fractional Yamabe problem, proposed by Gonzalez and Qing in 2013 as a nonlocal analogue of the famous Yamabe problem, is a geometric question which concerns the existence of a metric in a given conformal class whose associated fractional scalar curvature is constant. By conformal covariance of the fractional conformal Laplacian, it is reduced to solving a nonlocal elliptic equation with critical nonlinearity. In this talk, we first recall the history of the Yamabe problem and some geometric objects for which the fractional Yamabe problem makes sense. Then we observe how a solution to the equation can be achieved under various geometric conditions. Compactness or noncompactness of the solution set is also discussed. This talk is based on a collaboration with Monica Musso (PUC, Chile) and Juncheng Wei (UBC, Canada).
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