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The long-Time behavior of 3-dimensional Ricci flow on certain topologies
- Source :
- Journal fur die Reine und Angewandte Mathematik, vol 2017, iss 724, Journal für die reine und angewandte Mathematik (Crelles Journal), vol 2017, iss 725, Bamler, RH. (2017). The long-Time behavior of 3-dimensional Ricci flow on certain topologies. Journal fur die Reine und Angewandte Mathematik, 2017(724), 183-215. doi: 10.1515/crelle-2014-0101. UC Berkeley: Retrieved from: http://www.escholarship.org/uc/item/3sn06402
- Publication Year :
- 2017
- Publisher :
- eScholarship, University of California, 2017.
-
Abstract
- In this paper we analyze the long-time behavior of 3-dimensional Ricci flow with surgery. We prove that under the topological condition that the initial manifold only has non-aspherical or hyperbolic components in its geometric decomposition, there are only finitely many surgeries and the curvature is bounded by C t - 1 $t^{-1}$ for large t. This proves a conjecture of Perelman for this class of initial topologies. The proof of this fact illustrates the fundamental ideas that are used in the subsequent papers of the author.
- Subjects :
- Pure mathematics
Class (set theory)
Conjecture
Applied Mathematics
General Mathematics
010102 general mathematics
Ricci flow
Curvature
Network topology
01 natural sciences
Mathematics::Geometric Topology
Pure Mathematics
Manifold
Combinatorics
Bounded function
0103 physical sciences
010307 mathematical physics
Mathematics::Differential Geometry
0101 mathematics
Mathematics::Symplectic Geometry
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Journal fur die Reine und Angewandte Mathematik, vol 2017, iss 724, Journal für die reine und angewandte Mathematik (Crelles Journal), vol 2017, iss 725, Bamler, RH. (2017). The long-Time behavior of 3-dimensional Ricci flow on certain topologies. Journal fur die Reine und Angewandte Mathematik, 2017(724), 183-215. doi: 10.1515/crelle-2014-0101. UC Berkeley: Retrieved from: http://www.escholarship.org/uc/item/3sn06402
- Accession number :
- edsair.doi.dedup.....11eaab7a76951925cc99151cf58370fd