Surgery and equivariant Yamabe invariant

Details Surgery and equivariant Yamabe invariant Surgery and equivariant Yamabe invariant

2006-04-18

arxiv.org/abs/math/0604387v2

Mathematics

Differential Geometry

Scientific paper

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.

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