# 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} }

- Published 2013
DOI:10.2140/pjm.2013.266.1

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

#### Citations

##### Publications citing this paper.

SHOWING 1-10 OF 13 CITATIONS

## A note on solutions of Yamabe-type equations on products of spheres

VIEW 1 EXCERPT

CITES BACKGROUND

## Multipeak solutions for the Yamabe equation

VIEW 3 EXCERPTS

CITES BACKGROUND

## Bifurcation results for the Yamabe problem on Riemannian manifolds with boundary

VIEW 1 EXCERPT

CITES METHODS

## Bifurcation for the constant scalar curvature equation and harmonic Riemannian submersions

VIEW 1 EXCERPT

CITES BACKGROUND

## Metrics of constant scalar curvature on sphere bundles

VIEW 1 EXCERPT

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 22 REFERENCES

## On a deformation of Riemannian structures on compact manifolds

VIEW 17 EXCERPTS

HIGHLY INFLUENTIAL

## On bifurcation of solutions of the Yamabe problem in product manifolds

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Bifurcation and symmetry-breaking

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## On the number of constant scalar curvature metrics in a conformal class

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Einstein manifolds

#### Similar Papers

Loading similar papers…