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A Dual Yamabe Flow and Related Integral Flows |
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Citation: |
Jingang XIONG.A Dual Yamabe Flow and Related Integral Flows[J].Chinese Annals of Mathematics B,2024,45(3):319~348 |
Page view: 1053
Net amount: 562 |
Authors: |
Jingang XIONG; |
Foundation: |
the National Natural Science Foundation of China (Nos. 12325104,12271028) |
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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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