S¹-equivariant Yamabe invariant of 3-manifolds

2015/08/11 by Ammann, Bernd, Madani, Farid, Pilca, Mihaela · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1508.02727

Abstract

We show that the S¹-equivariant Yamabe invariant of the 3-sphere, endowed with the Hopf action, is equal to the (non-equivariant) Yamabe invariant of the 3-sphere. More generally, we establish a topological upper bound for the S¹-equivariant Yamabe invariant of any closed oriented 3-manifold endowed with an S¹-action. Furthermore, we prove a convergence result for the equivariant Yamabe constants of an accumulating sequence of subgroups of a compact Lie group acting on a closed manifold.

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• The toric CR Yamabe problem

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