Speaker: Liuwei Gong ，The Chinese University of Hong Kong

Inviter: 孙黎明

Title: Energy Estimates in Compactness and Convergence for Q-Curvature Problems

Language: English

Time & Venue: 2026.08.08 09:00-09:50 南楼N913

Abstract: The constant Q-curvature problem is a higher-order analogue of the Yamabe problem and exhibits many of similar phenomena, including concentration, bubbling, compactness, and geometric flows. In this talk, I will discuss two recent results on the fourth- and sixth-order constant Q-curvature problems. A common theme in both works is the use of precise energy estimates near bubbling configurations. In the compactness problem, these estimates help rule out blow-up below critical dimensions and identify the appearance of non-compactness in higher dimensions. In the flow problem, quantitative energy and stability estimates around bubbles, together with a Lojasiewicz–Simon type inequality, are used to control the long-time dynamics and prove convergence. I will explain how these energy methods connect the elliptic compactness theory with the dynamical behavior of Q-curvature flows. This talk is based on joint works with Seunghyeok Kim and Juncheng Wei, and with Sanghoon Lee and Juncheng Wei.