منابع مشابه
Dimensional Reduction and the Long-time Behavior of Ricci Flow
If g(t) is a three-dimensional Ricci flow solution, with sectional curvatures that are O(t) and diameter that is O(t 1 2 ), then the pullback Ricci flow solution on the universal cover approaches a homogeneous expanding soliton.
متن کاملOn the blow-up of four-dimensional Ricci flow singularities
In this paper we prove a conjecture by Feldman–Ilmanen–Knopf (2003) that the gradient shrinking soliton metric they constructed on the tautological line bundle over CP is the uniform limit of blow-ups of a type I Ricci flow singularity on a closed manifold. We use this result to show that limits of blow-ups of Ricci flow singularities on closed four-dimensional manifolds do not necessarily have...
متن کاملGeometrization of Three-dimensional Orbifolds via Ricci Flow
A three-dimensional closed orientable orbifold (with no bad suborbifolds) is known to have a geometric decomposition from work of Perelman [50, 51] in the manifold case, along with earlier work of Boileau-Leeb-Porti [4], Boileau-Maillot-Porti [5], BoileauPorti [6], Cooper-Hodgson-Kerckhoff [19] and Thurston [59]. We give a new, logically independent, unified proof of the geometrization of orbif...
متن کاملOn the Blow-up of Four Dimensional Ricci Flow Singularities
In this paper we prove a conjecture by Feldman-IlmanenKnopf in [14] that the gradient shrinking soliton metric they constructed on the tautological line bundle over CP is the uniform limit of blowups of a type I Ricci flow singularity on a closed manifold. We use this result to show that limits of blow-ups of Ricci flow singularities on closed four dimensional manifolds do not necessarily have ...
متن کاملTwo-dimensional Ricci flow as a stochastic process
We prove that, for a two-dimensional Riemannian manifold, the Ricci flow is obtained by a Wiener process.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pure and Applied Mathematics Quarterly
سال: 2013
ISSN: 1558-8599,1558-8602
DOI: 10.4310/pamq.2013.v9.n3.a2