2006/04/18 by Chanyoung Sung, Sung, Chanyoung
Mathematics · Medicine · #Geometry and complex manifolds #Bone and Joint Diseases #Advanced Mathematical Physics Problems
paper · pdf · doi:10.48550/arxiv.math/0604387
We consider the equivariant Yamabe problem, i.e. the Yamabe problem on the space of G-invariant metrics for a compact Lie group G. The G-Yamabe invariant is analogously defined as the supremum of the constant scalar curvatures of unit volume G-invariant metrics minimizing the total scalar curvature functional in their G-invariant conformal subclasses. We prove a formula about how the G-Yamabe invariant changes under the surgery of codimension 3 or more, and compute some G-Yamabe invariants.