The Logarithmic Sobolev Inequality Along the Ricci Flow: The Case $\lambda _0(g_0)=0$

Abstract

A uniform logarithmic Sobolev inequality, a uniform Sobolev inequality and a uniform $\kappa $-noncollapsing estimate along the Ricci flow are established in the situation that a certain smallest eigenvalue for the initial metric is zero.

Keywords

Uniform / Logarithmic Sobolev inequality / Sobolev inequality / Ricci flow / Eigenvalue

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