Eigenvalues and energy functionals with monotonicity formulae under Ricci flow |
| |
Authors: | Jun-Fang Li |
| |
Institution: | (1) The Mathematical Sciences Research Institute, 17 Gauss Way, Berkeley, CA 94720, USA |
| |
Abstract: | In this note, we construct families of functionals of the type of -functional and -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 Cao’s methods of eigenvalues (in Math Ann 337(2), 2007)
and improve their results. |
| |
Keywords: | 00A00 |
本文献已被 SpringerLink 等数据库收录! |
|