On the Nirenberg problem on spheres: Arbitrarily many solutions in a perturbative setting
报告题目(Title)：On the Nirenberg problem on spheres: Arbitrarily many solutions in a perturbative setting
报告人(Speaker)：Mohameden Ahmedou (Giessen Unniversity, Germany)
地点(Place)：后主楼 1124
时间(Time)：2023年7月7日 10:00-11:00
邀请人(Inviter)：Zhongwei Tang
报告摘要
Given a smooth positive function $K$ on the standard sphere $(\mathbb{S}^n,g_0)$, we use refined blow up analysis, Morse theoretical methods and counting index formulae to prove that, under generic conditions on the function $K$, there are arbitrarily many metrics $g$ conformally equivalent to $g_0$ and whose scalar curvature is given by the function $K$ provided that the function is sufficiently close to the scalar curvature of $g_0$. To prove such a multiplicity result we performed a refined blow up analysis of finite energy approximated solutions with non zero weak limit. This a joint work with M. Ben Ayed (Sfax University) and K. El Mehdi (Nouakchott University).
