REVIEW 35 cited by
Ricci flow with surgery on three-manifolds
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
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.
Forward citations
Cited by 35 Pith papers
-
Convergence of Finite Element Methods for Ricci Flow
A Regge/Lagrange finite element discretization of the 2D Ricci flow converges with O(h^{q+1}+h^{r+1}) error in the metric and Gaussian curvature.
-
Optimal decay constant for complete manifolds of positive scalar curvature with quadratic decay
An orientable 3-manifold with positive scalar curvature decaying at rate C > 2/3 must be a connected sum of spherical manifolds and S^2 x S^1 pieces, and the threshold 2/3 is optimal.
-
Global linearization of asymptotically stable systems without hyperbolicity
Asymptotically stable nonlinear systems admit global linearizing coordinates, smoothly off the equilibrium in every dimension except 5, where existence is equivalent to the smooth 4D Poincaré conjecture.
-
Exotic aspherical 4-manifolds
Constructs closed aspherical 4-manifolds that are homeomorphic but not diffeomorphic, providing counterexamples to the smooth Borel conjecture in dimension 4.
-
Volume Stability for Hyperbolic Manifolds and Applications to General Relativity
Near-minimizers of hyperbolic volume under R ≥ -6 converge to the hyperbolic metric in tensorial C^0 outside sets of vanishing volume.
-
The Ricci flow with prescribed curvature on graphs
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.
-
Expansion joints in hyperbolic manifolds
Cone-deforming an ideal arc through 'expansion joints' interpolates between stacked Borromean ring complements and lantern manifolds, and yields cone deformations of highly twisted 2-bridge unknotting tunnels.
-
Entanglement Spectrum Resolved by Loop Symmetries
Loop-symmetric many-body states have reduced density matrices that decompose into topological and geometric blocks computable from the Seifert–van Kampen theorem, giving exact entanglement spectra for Kitaev quantum d...
-
On the structure of noncollapsed Ricci flow limit spaces
Ricci flow limit spaces under bounded entropy have regular parts that form Ricci flow spacetimes and singular sets of codimension at least four.
-
Rigidity of Five-Dimensional shrinking gradient Ricci solitons
A five-dimensional shrinking gradient Ricci soliton with constant scalar curvature 1 and bounded curvature must be a finite quotient of R^3 × S^2.
-
Passing through nondegenerate singularities in mean curvature flows
Mean curvature flows through nondegenerate cylindrical singularities undergo an isolated, graphical surgery event whose topology change equals an (n-k)-surgery, matching Morse level sets.
-
Bordered hyperbolic manifolds with a fixed perimeter-to-volume ratio
For every n≥3 there are infinitely many pairwise incommensurable finite-volume hyperbolic n-manifolds with totally geodesic boundary sharing one fixed perimeter-to-volume ratio.
-
Gromov-Hausdorff convergence of time-slices of singular Ricci flows in dimension three
Proves Gromov-Hausdorff convergence of regular parts to time-slices in completed singular 3D Ricci flows plus structure results on the singular set.
-
The Ollivier Ricci flow with prescribed curvature on infinite graphs
Existence, uniqueness, and convergence of the Ollivier Ricci flow with prescribed curvature are established on infinite graphs with girth at least 6.
-
Closed $4$--Manifolds Foliated by Hyperplanes
Closed orientable 4-manifolds with transversely oriented C² codim-1 foliations by R³-leaves are homeomorphic to T⁴ (and diffeomorphic under an extra smooth 1-form condition).
-
Strong uniqueness and rectifiability of generalized cylindrical singularities in Ricci flow
Proves Lojasiewicz inequality for W-entropy near generalized cylinders in Ricci flow, yielding strong uniqueness of tangent flows and horizontal parabolic k-rectifiability of the corresponding singularity set.
-
$\kappa$-solutions with the round cylinder as an asymptotic shrinker
κ-solutions with round cylinder asymptotic shrinker are uniformly PIC, implying classification as the round shrinking cylinder, Bryant steady soliton, or Perelman's ancient solution.
-
Modifications of CMB Temperature and Polarization Quadrupole Signals in Thurston Spacetimes
Thurston spacetimes generate distinct evolving temperature and polarization patterns in the CMB that can be tracked via Stokes parameters and potentially isolated per geometry.
-
The Calabi flow with prescribed curvature on finite graphs
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.
-
Bianchi cosmologies in a Thurston-based theory of gravity
In a Thurston-geometry-dependent gravity theory, non-tilted BKS cosmologies admit shear-free perfect-fluid and static vacuum solutions for all topologies, isotropize under positive Lambda except for some Bianchi II ca...
-
Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow
Establishes a Lojasiewicz inequality for pointed W-entropy near cylindrical singularities in Ricci flow and applies it to prove strong uniqueness of the cylindrical tangent flow at the first singular time under a fixed gauge.
-
Well-posedness of Ricci Flow in Lorentzian Spacetime and its Entropy Formula
The paper extends Perelman's entropy functionals to 4D Lorentzian spacetimes and proves long-time well-posedness of Ricci flow using gradient flow properties of the coupled system.
-
Cosmological viability of anisotropic inflation in Thurston spacetimes
Inflationary models on Thurston geometries admit a stable anisotropic fixed point triggered by eccentricity-induced vector field coupling to the inflaton.
-
A large data result for vacuum Einstein's equations
Proves global well-posedness and smooth convergence of renormalized metrics to constant negative scalar curvature for large-data vacuum Einstein-Λ flow on negative Yamabe type 3-manifolds, confirming Ringström conject...
-
Bounds of Scalar curvature, S-curvature and distortion on $\infty$-Einstein Finsler manifolds
A Finsler-geometry paper proves growth estimates for S-curvature, distortion, and a new scalar curvature, but the main theorem relies on a stronger curvature bound than the one stated.
-
Navigating string theory field space with geometric flows
The authors define a flow-based distance for flux-supported internal spaces, modify the Ricci Flow Conjecture so towers of states appear only at fixed points at infinite distance, and construct flows for type II and 1...
-
Rigidity of Five-dimensional Shrinking Gradient Ricci Solitons with Constant Scalar Curvature
Every complete noncompact 5D gradient shrinking Ricci soliton with constant scalar curvature R=3λ splits as R²×S³ up to finite quotient.
-
On the structure of complete $G_2$-solitons
Proves compactness and convergence theorems for complete gradient G2-solitons under scalar curvature lower bounds and potential growth conditions.
-
Closed minimal surfaces of index one in Riemannian manifolds
Existence of index-one minimal hypersurfaces with unbounded volume in enlargeable manifolds (dims 3-7) plus 3D scalar curvature rigidity under area-nonincreasing maps.
-
Solutions to the Ricci Flow via Einstein Field Equations
Deforming the matter sector via quadratic stress-energy functionals maps solutions of Einstein field equations to solutions of the Ricci-Bourguignon flow.
-
Entropy and Non-Collapse in Lorentzian Geometry
Raychaudhuri flow is cast as a Lorentzian Ricci-flow analogue, yielding a claimed non-collapsing theorem and a geodesic entropy capacity bound on causal volume and information.
-
Metric--Measure Geometry and Geometric Analogues of Holographic Extremal Surfaces
The paper re-derives the standard weighted-area condition H=(1/2)∂_n f and labels it a holographic analogue; the example scales are inserted through hand-chosen f.
-
On the Parallels Between Minimal Surfaces and Einstein Four-Manifolds
This exposition restates known parallels; its new theorem overreaches, while the CP2 minimal immersion into S7 is a classical result.
-
Yang-Baxter Equation and Related Algebraic Structures
A reference monograph surveying skew braces, Rota-Baxter groups, quandles, and racks and their relationships to the Yang-Baxter equation.
-
Geometrisation of 3-manifolds
An overview of the geometrisation theorem for 3-manifolds that explains its content and effects in various situations.
Discussion (0). Continue with ORCID to comment.