A Dual Yamabe Flow and Related Integral Flows

Citation:

Jingang XIONG.A Dual Yamabe Flow and Related Integral Flows[J].Chinese Annals of Mathematics B,2024,45(3):319~348
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Authors:

Jingang XIONG;

Foundation:

the National Natural Science Foundation of China (Nos. 12325104,12271028)
Abstract: The author studies a family of nonlinear integral flows that involve Riesz potentials on Riemannian manifolds. In the Hardy-Littlewood-Sobolev (HLS for short) subcritical regime, he presents a precise blow-up profile exhibited by the flows. In the HLS critical regime, by introducing a dual Q curvature he demonstrates the concentrationcompactness phenomenon. If, in addition, the integral kernel matches with the Green’s function of a conformally invariant elliptic operator, this critical flow can be considered as a dual Yamabe flow. Convergence is then established on the unit spheres, which is also valid on certain locally conformally flat manifolds.

Keywords:

Hardy-Littlewood-Sobolev functional, Dual Q curvature, Integral flow

Classification:

45K05, 35B33
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