Éveline Legendre, Instituto Superior Técnico
Non-uniqueness of Sasaki toric metrics having constant scalar curvature

I will explain how the isoperimetric quotient, seen as a functional on sections of a strictly convex polyhedral cone, is related to constant scalar curvature Sasaki toric metric. I will point out the existence of two non-equivalent constant scalar curvature Sasaki toric metrics compatible with the same contact toric structure on $S^2\times S^3$.