Tianling Jin

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This paper is a continuation of our earlier work " [T. fractional Nirenberg problem, part I: blow up analysis and compactness of solutions, to appear in J. Eur. Math. Soc.] " , where compactness results were given on a fractional Nirenberg problem. We prove two existence results stated there. We also obtain a fractional Aubin inequality.
Making use of integral representations, we develop a unified approach to establish blow up profiles, compactness and existence of positive solutions of the conformally invariant equations P σ (v) = Kv n+2σ n−2σ on the standard unit sphere S n for all σ ∈ (0, n/2), where P σ is the intertwining operator of order 2σ. Finding positive solutions of these(More)
In this paper, we study existence, regularity, classification, and asymptotical behaviors of solutions of some Monge-Ampère equations with isolated and line singularities. We classify all solutions of det ∇ 2 u = 1 in R n with one puncture point. This can be applied to characterize ellipsoids, in the same spirit of Serrin's overdetermined problem for the(More)
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