# Ricci flow with surgery on three-manifolds

@article{Perelman2003RicciFW, title={Ricci flow with surgery on three-manifolds}, author={G. Perelman}, journal={arXiv: Differential Geometry}, year={2003} }

This is a technical paper, which is a continuation of math.DG/0211159. Here we construct Ricci flow with surgeries and verify most of the assertions, made in section 13 of that e-print: the exceptions are (1) the statement that manifolds that can collapse with local lower bound on sectional curvature are graph manifolds - this is deferred to a separate paper, since the proof has nothing to do with the Ricci flow, and (2) the claim on the lower bound for the volume of maximal horns and the… Expand

#### Paper Mentions

#### 1,018 Citations

Equivariant Ricci flow with surgery and applications to finite group actions on geometric 3-manifolds

- Mathematics
- 2008

Deforming three-manifolds with positive scalar curvature

- Mathematics, Physics
- 2009

#### References

SHOWING 1-10 OF 13 REFERENCES

Anderson Scalar curvature and geometrization conjecture for threemanifolds . Comparison Geometry (Berkeley, 1993-94), MSRI Publ

- Anderson Scalar curvature and geometrization conjecture for threemanifolds . Comparison Geometry (Berkeley, 1993-94), MSRI Publ
- 1997

Formation of singularities in the Ricci flow

- Surveys in Diff . Geom .
- 1995

Hamilton Formation of singularities in the Ricci flow. Surveys in Diff

- Geom
- 1995

Lawson Positive scalar curvature and the Dirac operator on complete Riemannian manifolds

- Publ. Math. IHES
- 1983