On the Nirenberg problem on spheres: Arbitrarily many solutions in a perturbative setting – Mohameden Ahmedou (Justus Liebig-Universität Gießen)


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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)

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