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.
Ricci flow with surgery on three-manifolds
7 Pith papers cite this work. Polarity classification is still indexing.
7
Pith papers citing it
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.
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2026 7verdicts
UNVERDICTED 7representative citing papers
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 Frechet mean estimation.
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.
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.
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 Weyl curvature on level sets of f are finite quotients of R^2 x S^{n-2}.
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.
Establishes several evolution formulas for functionals along the harmonic-Ricci flow on surfaces with boundary.
citing papers explorer
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The perturbative Ricci flow in gravity
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.
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Geometric Renyi Differential Privacy: Ricci Curvature Characterized by Heat Diffusion Mechanisms
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 Frechet mean estimation.
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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.
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On the Chern-Ricci form of a twisted almost K\"{a}hler structure
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.
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A note on Rigidity of Shrinking Gradient Ricci Solitons with Constant Scalar Curvature
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 Weyl curvature on level sets of f are finite quotients of R^2 x S^{n-2}.
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On weak formulations of (super) Ricci flows
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.
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Notes on harmonic-Ricci flow on surface
Establishes several evolution formulas for functionals along the harmonic-Ricci flow on surfaces with boundary.