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Juncheng Wei, The Chinese University of Hong Kong
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A Liouville theorem for fractional Lane-Emden systems is proven without assuming radial symmetry or decay, revealing a critical threshold for the existence of positive solutions.
The Yamabe problem's compactness transitions are precisely located, revealing dimension 14 as a critical threshold for general boundaries.
Non-locally-conformally-flat metrics on the ball can lead to infinitely many unbounded solutions for the boundary Yamabe equation, even with fixed background and prescribed curvatures.