Normal conformal metrics with prescribed Q-Curvature in $R^{2n}$

Speaker: 叶东 (华东师范大学)

Time: 2026-01-30 13:30-17:30
Location: 1110, SIMIS

Abstract:

We consider the Q-curvature equation
 $$(-\Delta)^n u=K(x) e^{2n u}  in  R^{2n} $$
where K is a non constant continuous function. Several studies are realized for the existence issue of normal conformal metrics with special Qcurvature in $R^4$, but there are few results for general non constant K and $n\geq 2$. Under mild growth control on K, we give a necessary condition on the total curvature Λu for any normal conformal metric $g_u=e^{2u}|dx|^2$ satisfying $Q_{g_u} = K$ in $R^{2n}$, or equivalently, solution with logarithmic growth at infinity. Inversely, when K is nonpositive satisfying polynomial growth control, we show the existence of normal conformal metrics with quasi optimal range of total curvature and precise asymptotic behavior at infinity.

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About Speaker:

叶东教授是华东师范大学数学科学学院教授、博士生导师，国家级人才项目入选者。他于1990年获武汉大学学士学位，1991年和1994年分别获得巴黎大学理学硕士学位与卡尚高等师范学校博士学位。1994年至2018年先后在法国塞尔吉-蓬图瓦斯大学、洛林大学任教，2018年全职回国加入华东师范大学。其研究方向聚焦于微分几何及物理中的非线性偏微分方程，在Invent. Math.，Adv. Math., Math. Ann., Ann. Inst. H. Poincare–AN, JFA, Calc. Var. PDEs等国际期刊发表论文60余篇，主持科技部重点研发计划等项目。