Affiliation:
1. School of Mathematics and Statistics , Wuhan University , Wuhan 430072 , P. R. China
Abstract
Abstract
By using the monotonicity of the log Sobolev functionals, we prove a no breathers theorem for noncompact harmonic Ricci flows under conditions on infimum of log Sobolev functionals and curvatures. As an application, we obtain a no breathers theorem for noncompact harmonic Ricci flows with asymptotically nonnegative Ricci curvature.
Funder
National Natural Science Foundation of China
Subject
Applied Mathematics,Analysis
Reference14 articles.
1. J. R. Chen and Q. Chen,
A Perelman-type no shrinking breather theorem for noncompact harmonic Ricci flows,
preprint (2021), https://www.mis.mpg.de/publications/preprints/2021/prepr2021-19.html.
2. L. Cheng and Y. Zhang,
Perelman-type no breather theorem for noncompact Ricci flows,
Trans. Amer. Math. Soc. 374 (2021), no. 11, 7991–8012.
3. L. Cheng and Y. Zhang,
A no expanding breather theorem for noncompact Ricci flows,
Ann. Global Anal. Geom. 61 (2022), no. 3, 519–529.
4. C. B. Croke,
Some isoperimetric inequalities and eigenvalue estimates,
Ann. Sci. Éc. Norm. Supér. (4) 13 (1980), no. 4, 419–435.
5. E. Hebey,
Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities,
Courant Lect. Notes Math. 5,
New York University, New York, 2000.