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.
Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
7 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Let M be a closed oriented three-manifold, whose prime decomposition contains no aspherical factors. We show that for any initial riemannian metric on M the solution to the Ricci flow with surgery, defined in our previous paper math.DG/0303109, becomes extinct in finite time. The proof uses a version of the minimal disk argument from 1999 paper by Richard Hamilton, and a regularization of the curve shortening flow, worked out by Altschuler and Grayson.
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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.
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.
The monograph organizes and derives classical Riemannian geometry structures explicitly in coordinate and matrix form for direct use in optimization algorithms on nonlinear manifolds.
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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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.
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Foundations of Riemannian Geometry for Riemannian Optimization: A Monograph with Detailed Derivations
The monograph organizes and derives classical Riemannian geometry structures explicitly in coordinate and matrix form for direct use in optimization algorithms on nonlinear manifolds.