报告题目：Some existence and compactness results related to prescribed fractional Q-curvatures problems

报 告 人：唐仲伟 教授

报告人所在单位：北京师范大学数学科学学院

报告日期：2024-09-12

报告时间：10:00

报告地点：光华东主楼2201

报告摘要：In this talk, I present some results about the compactness and existence results of the solutions to the prescribing fractional Q-curvature problem. At first, we consider the fractional order is 2σ on n-dimensional standard sphere when n − 2σ = 2, σ = 1 + m/2, m ∈ N+. The compactness results are novel and optimal. In addition, we proved a degree-counting formula of all solutions to achieve the existence. From our results, we can know where blow up occur. Furthermore, the sequence of solutions that blow up precisely at any finite distinct location can be constructed. It is worth noting that our results include the case of multiple harmonic. Secondly, by combining critical points at infinity approach with Morse theory we obtain new existence results under suitable pinching conditions. This is a joint work with Dr. Yan Li and Ning Zhou.

个人简介：唐仲伟，男，1976年生，教授，博士生导师，现担任北京师范大学数学科学学院党委书记、教学指导委员会主任。2004年在中国科学院数学与系统科学研究院应用数学所获得博士学位， 2007年9月-2009年9月受德国洪堡基金会资助在德国吉森大学做洪堡学者，自2004年8月起在北京师范大学数学科学学院工作。主要研究领域为偏微分方程及非线性分析，在IMRN,JFA,Nonlinearity, Calc. Var. Partial Differential Equations, J. Differential Equations，Pacific J. Math.等期刊上发表SCI论文70余篇，主持国家自然科学基金6项。