The (logarithmic) Sobolev inequalities along geometric flow and applications

Abstract

For some class of geometric flows, we obtain the (logarithmic) Sobolev inequalities and their equivalence up to different factors directly and also obtain the long time non-collapsing and non-inflated properties, which generalize the results in the case of Ricci flow or List-Ricci flow or harmonic-Ricci flow. As applications, for mean curvature flow in Lorentzian space with nonnegative sectional curvature and twisted Kähler-Ricci flow on Fano manifolds, we get the results above.

35pages,correct some typos

References in corpus (8)

• Ricci flow with surgery on three-manifolds
• The logarithmic Sobolev inequality along the Ricci flow
• Space of Ricci flows (II)
• Convergence of a Kähler-Ricci flow
• Uniform Sobolev inequalities for manifolds evolving by Ricci flow
• A uniform Sobolev inequality under Ricci flow
• The logarithmic Sobolev inequality along the Ricci flow in dimension 2
• An upper bound of the heat kernel along the harmonic-Ricci flow

Cited by in corpus (1)

• Smooth long-time existence of Harmonic Ricci Flow on surfaces