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Seminar
FIELD Math:Geometry
DATE May 12 (Thu), 2022
TIME 10:00-11:00
PLACE Online
SPEAKER Henry, Guillermo
HOST Shin, Jinwoo
INSTITUTE Universidad de Buenos Aires
TITLE Solutions of the Yamabe equation induced by subgroups of isometries and isoparametric functions
ABSTRACT Given a closed $n-$dimensional Riemannian manifold $(M,g)$ with scalar curvature $s_g$. We say that $u$ is a solution of the Yamabe equation if for some constant $c$ it holds $$\frac{4(n-1)}{(n-2)}\Delta_g u+s_gu=c|u|^{\frac{4}{n+2}}u.$$
The solutions of this equation are interesting because they are related with metrics of constant scalar curvature in the conformal class of $g$.
In this talk we are going to discuss some results on the existence of positive and sign-changing solutions of the Yamabe equation obtained by considering either the action of a subgroup of isometries or an isoparametric foliation.
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