Monotone volume formulas for geometric flows

DOI10.1515/CRELLE.2010.044zbMath1204.53054arXiv0905.2328OpenAlexW3102752062WikidataQ125988873 ScholiaQ125988873MaRDI QIDQ3577942

Reto Muller

Publication date: 13 July 2010

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.2328

zbMATH Keywords

mean curvature flowRicci flowList's flowmonotonicity formulaharmonic map flowreduced volume

Mathematics Subject Classification ID

Related Items (28)

Harnack estimates for Ricci flow on a warped product ⋮ Local curvature estimates for the Ricci-harmonic flow ⋮ Long time existence of Ricci-harmonic flow ⋮ Harnack estimates for heat equations with potentials on evolving manifolds ⋮ Liouville theorem for heat equation Along ancient super Ricci flow via reduced geometry ⋮ 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 ⋮ A no shrinking breather theorem for noncompact harmonic Ricci flows ⋮ Gaussian upper bounds for the heat kernel on evolving manifolds ⋮ Differential Harnack inequalities for heat equations with potentials under geometric flows ⋮ Unnamed Item ⋮ Harnack estimates for nonlinear backward heat equations in geometric flows ⋮ Geometric flows and differential Harnack estimates for heat equations with potentials ⋮ Monotonicity of functionals along conformal Ricci flow ⋮ Harnack estimates for conjugate heat kernel on evolving manifolds ⋮ Sharp logarithmic Sobolev inequalities along an extended Ricci flow and applications ⋮ Long time existence and bounded scalar curvature in the Ricci-harmonic flow ⋮ On \(f\)-non-parabolic ends for Ricci-harmonic metrics ⋮ Harnack estimates for geometric flows, applications to Ricci flow coupled with harmonic map flow ⋮ Generalized Ricci flow. II. Existence for complete noncompact manifolds ⋮ On Ricci-harmonic metrics ⋮ Liouville theorems for harmonic map heat flow along ancient super Ricci flow via reduced geometry ⋮ On the entropy formulas and solitons for the Ricci-harmonic flow ⋮ Differential Harnack estimates for backward heat equations with potentials under geometric flows ⋮ Liouville type theorems and gradient estimates for nonlinear heat equations along ancient \(K\)-super Ricci flow via reduced geometry ⋮ Gap theorems for Ricci-harmonic solitons ⋮ Sobolev-type inequalities and heat kernel bounds along the geometric flow

Cites Work

• Notes on Perelman's papers

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