Multiplicity of solutions to the Yamabe problem on collapsing Riemannian submersions

@inproceedings{Bettiol2013MultiplicityOS,
  title={Multiplicity of solutions to the Yamabe problem on collapsing Riemannian submersions},
  author={Renato G. Bettiol and Paolo Piccione},
  year={2013}
}
Let g_t be a family of constant scalar curvature metrics on the total space of a Riemannian submersion obtained by shrinking the fibers of an original metric g, so that the submersion collapses as t approaches 0 (i.e., the total space converges to the base in the Gromov-Hausdorff sense). We prove that, under certain conditions, there are at least 3 unit volume constant scalar curvature metrics in the conformal class [g_t] for infinitely many t's accumulating at 0. This holds, e.g., for… CONTINUE READING

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