Evolution of an extended Ricci flow system

DOI10.4310/CAG.2008.v16.n5.a5zbMath1166.53044OpenAlexW2076863809WikidataQ125881052 ScholiaQ125881052MaRDI QIDQ1011996

Bernhard List

Publication date: 14 April 2009

Published in: Communications in Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/cag.2008.v16.n5.a5

zbMATH Keywords

entropya priori estimatesRicci flowinjectivity radiusEinstein vacuum equationssurgeryconstraint equationscompactness theoremancient solutionsshort time existenceBartnik' s quasi-local mass.initial data setsmonotonicity formula for flownoncollapsing result

Mathematics Subject Classification ID

Related Items (65)

Evolution and monotonicity of geometric constants along the extended Ricci flow ⋮ On the rigidity of harmonic-Ricci solitons ⋮ GRAVITY-ASSISTED SOLUTION OF THE MASS GAP PROBLEM FOR PURE YANG–MILLS FIELDS ⋮ Yamabe flow and ADM mass on asymptotically flat manifolds ⋮ An upper bound of the heat kernel along the harmonic-Ricci flow ⋮ Harnack estimates for Ricci flow on a warped product ⋮ Monotonicity formulas of eigenvalues and energy functionals along the rescaled List's extended Ricci flow ⋮ On convergence criteria for the coupled flow of Li-Yuan-Zhang ⋮ Local curvature estimates for the Ricci-harmonic flow ⋮ Basic structural equations for almost Ricci-harmonic solitons and applications ⋮ Long time existence of Ricci-harmonic flow ⋮ On the relation between Ricci-harmonic solitons and Ricci solitons ⋮ Volume growth for gradient shrinking solitons of Ricci-harmonic flow ⋮ Harnack estimates for heat equations with potentials on evolving manifolds ⋮ Scalar curvature bound and compactness results for Ricci harmonic solitons ⋮ Lower bounds for the scalar curvature of noncompact gradient solitons of List's flow ⋮ Evolution of eigenvalues of geometric operator under the rescaled List's extended Ricci flow ⋮ Volume growth of shrinking gradient Ricci-harmonic soliton ⋮ Differential Harnack inequalities under a coupled Ricci flow ⋮ Unnamed Item ⋮ Heat Kernel Estimates Under the Ricci–Harmonic Map Flow ⋮ Harnack estimates for nonlinear heat equations with potentials in geometric flows ⋮ The (logarithmic) Sobolev inequalities along geometric flow and applications ⋮ Hyper-elastic Ricci flow: Gradient flow, local existence-uniqueness, and a Perelman energy functional ⋮ Static flow on complete noncompact manifolds. I: Short-time existence and asymptotic expansions at conformal infinity ⋮ Conditions to extend the Ricci flow coupled with harmonic map flow ⋮ Gradient Ricci-harmonic solitons on multiply warped products ⋮ Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvatures ⋮ Mean curvature flow in an extended Ricci flow background ⋮ Aronson–Bénilan estimates for weighted porous medium equations under the geometric flow ⋮ Gaussian upper bounds for the heat kernel on evolving manifolds ⋮ Gradient estimates for a weighted parabolic equation under geometric flow ⋮ Regularity and curvature estimate for List's flow in four dimension ⋮ Singularity of connection Ricci flow for three-manifolds ⋮ On the extension of the harmonic Ricci flow ⋮ Regularity and compactness of harmonic-Einstein equations ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Harnack estimates for nonlinear backward heat equations in geometric flows ⋮ Differential Harnack inequality for the nonlinear heat equations ⋮ Geometric flows and differential Harnack estimates for heat equations with potentials ⋮ Local curvature estimates for the Laplacian flow ⋮ Monotonicity of functionals along conformal Ricci flow ⋮ Eigenvalues of the weighted Laplacian under the extended Ricci flow ⋮ Sharp logarithmic Sobolev inequalities along an extended Ricci flow and applications ⋮ Long time existence and bounded scalar curvature in the Ricci-harmonic flow ⋮ Evolution of the Yamabe constant under Bernhard List's flow ⋮ On \(f\)-non-parabolic ends for Ricci-harmonic metrics ⋮ Harnack estimates for geometric flows, applications to Ricci flow coupled with harmonic map flow ⋮ A Gaussian upper bound of the conjugate heat equation along Ricci-harmonic flow ⋮ On Perelman's dilaton ⋮ An entropy formula for the heat equation on manifolds with time-dependent metric, application to ancient solutions ⋮ Differential Harnack inequalities for the backward heat equation with potential under the harmonic-Ricci flow ⋮ Total mass under connection Ricci flow ⋮ On Ricci-harmonic metrics ⋮ Unnamed Item ⋮ Ricci soliton vector fields of spherically symmetric static spacetimes ⋮ Gap theorems for compact almost Ricci-harmonic solitons ⋮ On the extension of Ricci harmonic flow ⋮ Monotonicity formulas for the first eigenvalue of the weighted \(p\)-Laplacian under the Ricci-harmonic flow ⋮ On the spectrum of the weighted \(p\)-Laplacian under the Ricci-harmonic flow ⋮ On the entropy formulas and solitons for the Ricci-harmonic flow ⋮ A convergence result of Ricci flow on \(\mathbb{R}^{3}\) with warped product metric ⋮ Gap theorems for Ricci-harmonic solitons ⋮ Sobolev-type inequalities and heat kernel bounds along the geometric flow

This page was built for publication: Evolution of an extended Ricci flow system