Prescribing scalar curvatures: on the negative Yamabe case

发布时间：2023-12-13 作者：浏览次数：

Speaker:	朱超娜	DateTime:	2023年12月15日（周五）上午9:00-10:00
Brief Introduction to Speaker: 朱超娜，罗马第二大学博士后。2019年博士毕业于中国科学技术大学数学科学学院，2019年至2022年在中国科学院数学与系统科学研究院做博士后。主要研究方向为Dirac调和映照的紧性、正则性，及临界半线性方程解的存在性。部分成果发表在Tran AMS，CVPDE，Sci China Math等杂志上。		Place:	6号楼2楼报告厅
Abstract:The problem of prescribing conformally the scalar curvature on a closed Riemannian manifold of negative Yamabe invariant is always solvable, if the function to be prescribed is strictly negative, while sufficient and necessary conditions are known in the case that function is non-positive. Still in the case of a negative Yamabe invariant, Rauzy showed solvability, if the function to be prescribed is not too positive. In this talk we will review these results variationally, quantify the principle existence result of Rauzy and show under additional assumptions, that for a sign changing prescribed function solutions to the conformally prescribed scalar curvature problem, while existing, are not unique. In collaboration with Martin Mayer.