Quantitative stability of the total Q-curvature functional
数学专题报告
报告题目(Title)：Quantitative stability of the total Q-curvature functional
报告人(Speaker)：Jesse Ratzkin(Universität Würzburg)
地点(Place)：Zoom ID：947 2279 1613, PWD: 552593
时间(Time)：2024 年 10月 24日 16：00—17：00
邀请人(Inviter)：熊金钢
报告摘要
I will discuss recent work with João Henrique Andrade, Tobias König and Juncheng Wei exploring the stability of the minimizing set of the total Q-curvature functional. The Q-curvature of order k of a Riemannian metric is an analog of the scalar curvature, except that it transforms according to a PDE of order 2k under a conformal change. Thus, just as in the scalar curvature setting, one can minimize the volume-normalized total Q-curvature to produce conformal invariants. We show that the distance of a metric to the minimizing set is controlled by a power of the Q-curvature deficit. Generically this exponent is two, but we also produce interesting examples such that the exponent is strictly larger than two.
* This PDE seminar is co-organized with Tianling Jin at HKUST and Juncheng Wei at CUHK. See the seminar webpage: https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
