An integral equation in conformal geometry
Fengbo Hang, Xiaodong Wang, Xiaodong Yan · Annales de l Institut Henri Poincaré C Analyse Non Linéaire · 2007
Motivated by Carleman's proof of the isoperimetric inequality in the plane, we study the problem of finding a metric with zero scalar curvature maximizing the isoperimetric ratio among all zero scalar curvature metrics in a fixed conformal class on a compact manifold with boundary. We derive a criterion for the existence and make a related conjecture.