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.
| Original language | English |
|---|---|
| Article number | 19800 |
| Pages (from-to) | 729-764 |
| Number of pages | 36 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 434 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Feb 2016 |
Keywords
- Geometric flow
- Logarithmic Sobolev inequality
- Lorentzian mean curvature flow
- Sobolev inequality
- Twisted Kähler-Ricci flow
Fingerprint
Dive into the research topics of 'The (logarithmic) Sobolev inequalities along geometric flow and applications'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver