Harmonically free group actions and equivariant bifurcation in the Yamabe problem

TL;DR

This paper investigates the multiplicity of constant scalar curvature metrics on product manifolds with boundary, employing equivariant bifurcation theory to understand how symmetries influence solutions.

Contribution

It introduces a novel application of equivariant bifurcation theory to the Yamabe problem on manifolds with boundary, highlighting the role of harmonic group actions.

Findings

Identifies conditions for multiple solutions with constant scalar curvature.

Shows how group symmetries affect bifurcation points.

Provides new insights into geometric analysis of manifolds with boundary.

Abstract

We study multiplicity of constant scalar curvature metrics in products of a compact closed manifold and a compact manifold with boundary using equivariant bifurcation theory.