Ricci flow of almost non-negatively curved three manifolds
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Miles Simon
Abstract
In this paper we study the evolution of almost non-negatively curved (possibly singular) three dimensional metric spaces by Ricci flow. The non-negatively curved metric spaces which we consider arise as limits of smooth Riemannian manifolds (Mi, ig), i ∈ ℕ, whose Ricci curvature is bigger than –1/i, and whose diameter is less than d0 (independent of i) and whose volume is bigger than v0 > 0 (independent of i). We show for such spaces, that a solution to Ricci flow exists for a short time t ∈ (0, T), that the solution is smooth for t > 0, and has Ricci (g(t)) ≧ 0 and Riem (g(t)) ≧ c/t for t ∈ (0, T) (for some constant c = c(v0, d0, n)). This allows us to classify the topological type and the differential structure of the limit manifold (in view of the theorem of Hamilton [J. Diff. Geom. 24: 153–179, 1986] on closed three manifolds with non-negative Ricci curvature).
© Walter de Gruyter Berlin · New York 2009
Articles in the same Issue
- Gröbner geometry of vertex decompositions and of flagged tableaux
- The Diophantine equation aX4 – bY2 = 1
- C*-algebras and self-similar groups
- Conjugate varieties with distinct real cohomology algebras
- Classification of hyperfinite factors up to completely bounded isomorphism of their preduals
- Ricci flow of almost non-negatively curved three manifolds
- Linear dependence in Mordell-Weil groups
Articles in the same Issue
- Gröbner geometry of vertex decompositions and of flagged tableaux
- The Diophantine equation aX4 – bY2 = 1
- C*-algebras and self-similar groups
- Conjugate varieties with distinct real cohomology algebras
- Classification of hyperfinite factors up to completely bounded isomorphism of their preduals
- Ricci flow of almost non-negatively curved three manifolds
- Linear dependence in Mordell-Weil groups
