Speaker: 朱超娜教授，宁波大学

Inviter: 孙黎明

Title: Existence of prescribing scalar curvature problem on the negative Yamabe case

Language: Chinese

Time & Venue: 2026.04.24 10:00-11:00 思源楼 S817

Abstract: The problem of prescribing conformally the scalar curvature on a closed 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, show the existence of minimizability under smallness assumptions on K+ =max{K, 0} and talk what happens when the relevant arguments fail to apply. At last, we will construct a function, for which saddle point solutions to the conformally prescribed scalar curvature problem still exist. In collaboration with Martin Mayer.