The (logarithmic) Sobolev inequalities along geometric flow and applications

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:434

Article

Fang, Shouwen¹  Zheng, Tao² 

[1] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Jiangsu, Peoples R China

[2] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

关键词: Geometric flow;    Twisted Kahler-Ricci flow;    Lorentzian mean curvature flow;    Logarithmic Sobolev inequality;    Sobolev inequality;   

DOI  :  10.1016/j.jmaa.2015.09.034

来源: Elsevier

【 摘 要 】

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 Kahler-Ricci flow on Fano manifolds, we get the results above. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free