Nodal solutions of the Yamabe equation
报告题目(Title)：Nodal solutions of the Yamabe equation
报告人(Speaker)：Guillermo Henry (Universidad de Buenos Aires, Argentina)
地点(Place)：后主楼1220
时间(Time)：6月11日上午10:00-11:00
邀请人(Inviter)：彦文娇
报告摘要
In this talk we will discuss about existence results of nodal solutions of the Yamabe equation
on closed connected Riemannian manifolds.Let $(M^n,g)$ be a Riemannian manifold of dimension $n\geq 3$,
we say that $u$ is a nodal solution of the Yamabe equation if satisfies for some constant $c$ the non-linear
elliptic equation $$\frac{4(n-1)}{n-2}\Delta_{g}u+s_gu=c|u|^{\frac{4}{n-2}}u$$ and $u$ changes sign.
A positive solution of the Yamabe equation induces a constant scalar curvature metric. For nodal
solutions there is not an immediate geometric interpretation. However, they are very interesting from
the analytic point of view and have gained lot of attention in the last years.
