pith. machine review for the scientific record. sign in

arxiv: math/0303109 · v1 · submitted 2003-03-10 · 🧮 math.DG

Recognition: unknown

Ricci flow with surgery on three-manifolds

Authors on Pith no claims yet
classification 🧮 math.DG
keywords flowricciboundlowermanifoldsotherassertionsclaim
0
0 comments X
read the original abstract

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 smoothness of solutions from some time on, which turned out to be unjustified and, on the other hand, irrelevant for the other conclusions.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The perturbative Ricci flow in gravity

    hep-th 2026-04 unverdicted novelty 8.0

    A perturbative Ricci-flow formulation in gravity yields a renormalization scheme for Newton's constant that exhibits a non-Gaussian fixed point at two-loop order.

  2. Geometric Renyi Differential Privacy: Ricci Curvature Characterized by Heat Diffusion Mechanisms

    stat.ML 2026-04 unverdicted novelty 7.0

    Renyi differential privacy for manifold-valued data is characterized via dimension-free Harnack inequalities and governed by Ricci curvature, with heat diffusion and Langevin mechanisms plus application to private Fre...

  3. The Ricci flow with prescribed curvature on graphs

    math.DG 2026-03 unverdicted novelty 7.0

    A discrete Ricci flow on graphs converges exponentially to prescribed Lin-Lu-Yau curvatures iff attainable, with an explicit max-edge-density condition for constant curvature on girth-at-least-6 graphs.

  4. Modifications of CMB Temperature and Polarization Quadrupole Signals in Thurston Spacetimes

    gr-qc 2026-05 unverdicted novelty 6.0

    Thurston spacetimes generate distinct evolving temperature and polarization patterns in the CMB that can be tracked via Stokes parameters and potentially isolated per geometry.

  5. On the Chern-Ricci form of a twisted almost K\"{a}hler structure

    math.DG 2026-04 unverdicted novelty 6.0

    An explicit formula is given for the local connection 1-form α on the anti-canonical bundle of a twisted almost Kähler structure, yielding the Chern-Ricci form as ρ = -dα.

  6. The Calabi flow with prescribed curvature on finite graphs

    math.DG 2026-04 unverdicted novelty 6.0

    The Calabi flow on finite graphs converges globally if and only if a weight function exists realizing the prescribed curvature, with convergence for constant curvature under topological conditions.

  7. A note on Rigidity of Shrinking Gradient Ricci Solitons with Constant Scalar Curvature

    math.DG 2026-04 unverdicted novelty 5.0

    Shrinking gradient Ricci solitons with constant scalar curvature k/2, nonnegative Ricci curvature and sectional curvature bounded by 1/(2(k-1)) are finite quotients of R^{n-k} x S^k; those with R=(n-2)/2 and vanishing...

  8. On weak formulations of (super) Ricci flows

    math.DG 2026-04 unverdicted novelty 5.0

    Smooth compact Ricci flows are characterized weakly solely via metrics and measures by defining super Ricci flows and adding a saturation condition to recover equality.

  9. Notes on harmonic-Ricci flow on surface

    math.DG 2026-05 unverdicted novelty 2.0

    Establishes several evolution formulas for functionals along the harmonic-Ricci flow on surfaces with boundary.