Let R be a constant. Let MγR be the space of smooth metrics g on a given compact manifold Ωn (n ≥ 3) with smooth boundary S such that g has constant scalar curvature R and g|ε is a fixed metric γ on S. Let V (g) be the volume of g ε MγR . In this work, we classify all Einstein or conformally flat metrics which are critical points of V (.) in MγR.
ASJC Scopus subject areas
- Applied Mathematics