A Dual Yamabe Flow and Related Integral Flows  

作　　者：Jingang XIONG 

机构地区：[1]School of Mathematical Sciences,Laboratory of Mathematics and Complex Systems,Ministry of Education,Beijing Normal University,Beijing 100875,China

出　　处：《Chinese Annals of Mathematics,Series B》2024年第3期319-348,共30页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.12325104,12271028).

摘　　要：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.

关 键 词：Hardy-Littlewood-Sobolev functional Dual Q curvature Integral flow 

分 类 号：O186.12[理学—数学]