Abstract

In this talk, I will discuss some relationships among the positivity of Q-curvature, scalar curvature, and Ricci curvature on conformally flat manifolds. Under positivity conditions on the top-order Q-curvature and the scalar curvature, we establish integral growth estimates for all lower-order Q-curvatures over geodesic balls. Additionally, we derive growth bounds for Ricci curvature on geodesic balls, which are related to a conjecture of Yau. This is joint work with Juncheng Wei and Xingwang Xu.

Biography

Mingxiang Li is currently a postdoctoral fellow at The Chinese University of Hong Kong, starting in September 2024, under the supervision of Prof. Juncheng Wei. He received his bachelor’s degree in 2019 and his Ph.D. in 2024 from Nanjing University, where he was advised by Prof. Xingwang Xu. His research focuses on partial differential equations and geometric analysis, particularly conformal geometry. 

Zoom meeting

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