Eigenvalues and energy functionals with monotonicity formulae under Ricci flow
| dc.creator | Li, Junfang | |
| dc.date | 2007-01-19 | |
| dc.date | 2007-01-26 | |
| dc.date.accessioned | 2026-07-07T07:43:00Z | |
| dc.date.available | 2026-07-07T07:43:00Z | |
| dc.description | In this note, we construct families of functionals of the type of $\mathcal{F}$-functional and $\mathcal{W}$-functional of Perelman. We prove that these new functionals are nondecreasing under the Ricci flow. As applications, we give a proof of the theorem that compact steady Ricci breathers must be Ricci-flat. Using these new functionals, we also give a new proof of Perelman's no non-trivial expanding breather theorem. Furthermore, we prove that compact expanding Ricci breathers must be Einstein by a direct method. In this note, we also extend X. Cao's methods of eigenvalues\cite{C} and improve their results. | |
| dc.description | 19 pages, one reference added, to appear in Mathematische Annalen | |
| dc.identifier | https://arxiv.org/abs/math/0701548 | |
| dc.identifier | http://arxiv.org/abs/math/0701548 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122658 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 53C44; 35K55 | |
| dc.title | Eigenvalues and energy functionals with monotonicity formulae under Ricci flow | |
| dc.type | text |