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arXiv · 1502.02305

The (logarithmic) Sobolev inequalities along geometric flow and applications

Shouwen Fang·Tao Zheng
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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 K\"ahler-Ricci flow on Fano manifolds, we get the results above.

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Shouwen Fang, Tao Zheng. 2015-02-08. The (logarithmic) Sobolev inequalities along geometric flow and applications. https://arxiv.org/abs/1502.02305

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