Open main menu
Home
Random
Recent changes
Special pages
Community portal
Preferences
About Wikipedia
Disclaimers
Incubator escapee wiki
Search
User menu
Talk
Dark mode
Contributions
Create account
Log in
Editing
Ricci flow
(section)
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
== References == '''Articles for a popular mathematical audience.''' *{{cite journal|last1=Anderson|first1=Michael T.|title=Geometrization of 3-manifolds via the Ricci flow|journal=Notices Amer. Math. Soc.|volume=51|issue=2|year=2004|pages=184–193|mr=2026939|url=https://www.ams.org/journals/notices/200402/fea-anderson.pdf}} *{{cite journal|last1=Milnor|first1=John|title=Towards the Poincaré Conjecture and the classification of 3-manifolds|journal=Notices Amer. Math. Soc.|volume=50|year=2003|issue=10|pages=1226–1233|mr=2009455|url=https://www.ams.org/notices/200310/fea-milnor.pdf}} *{{cite journal|last1=Morgan|first1=John W.|title=Recent progress on the Poincaré conjecture and the classification of 3-manifolds|journal=Bull. Amer. Math. Soc. (N.S.)|volume=42|year=2005|issue=1|pages=57–78|mr=2115067|doi=10.1090/S0273-0979-04-01045-6|doi-access=free}} *{{Cite book|last=Tao|first=T.|author-link=Terence Tao|chapter=Ricci flow|pages=279–281|chapter-url=http://terrytao.files.wordpress.com/2008/03/ricci.pdf|title=The Princeton Companion to Mathematics|editor1-first=Timothy|editor1-last=Gowers|editor1-link=Timothy Gowers|editor2-first=June|editor2-last=Barrow-Green|editor3-first=Imre|editor3-last=Leader|editor3-link=Imre Leader|year=2008|publisher=Princeton University Press|isbn=978-0-691-11880-2|title-link=The Princeton Companion to Mathematics|ref=atest}} '''Research articles.''' *{{cite journal |last1=Böhm |first1=Christoph |last2=Wilking |first2=Burkhard |s2cid=15521923 |title=Manifolds with positive curvature operators are space forms |journal=Ann. of Math. (2) |date=2008 |volume=167 |issue=3 |pages=1079–1097|doi=10.4007/annals.2008.167.1079 |mr=2415394|jstor=40345372|arxiv=math/0606187}} *{{cite journal |last1=Brendle |first1=Simon |s2cid=438716 |title=A general convergence result for the Ricci flow in higher dimensions |journal=Duke Math. J. |date=2008 |volume=145 |issue=3 |pages=585–601|mr=2462114|author-link=Simon Brendle|doi=10.1215/00127094-2008-059|zbl=1161.53052|url=https://projecteuclid.org/euclid.dmj/1229349905|arxiv=0706.1218}} *{{cite journal |last1=Brendle |first1=Simon |last2=Schoen |first2=Richard |s2cid=2901565 |title=Manifolds with 1/4-pinched curvature are space forms |journal=J. Amer. Math. Soc. |date=2009 |volume=22 |issue=1 |pages=287–307|doi=10.1090/S0894-0347-08-00613-9 |mr=2449060|author1-link=Simon Brendle|author2-link=Richard Schoen|jstor=40587231|arxiv=0705.0766|bibcode=2009JAMS...22..287B }} *{{cite journal | first = Huai-Dong | last = Cao | author-link = Huai-Dong Cao |author2=Xi-Ping Zhu | title = A Complete Proof of the Poincaré and Geometrization Conjectures — application of the Hamilton-Perelman theory of the Ricci flow | url = http://www.ims.cuhk.edu.hk/~ajm/vol10/10_2.pdf | journal = Asian Journal of Mathematics | volume = 10 |date=June 2006 | issue =2| author2-link = Xi-Ping Zhu|mr=2488948}} [https://web.archive.org/web/20120514194801/http://www.intlpress.com/AJM/p/2006/10_2/AJM-10-2-Erratum.pdf Erratum]. ** Revised version: {{cite arXiv | eprint=math.DG/0612069 |title=Hamilton-Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture | author1=Huai-Dong Cao | author2=Xi-Ping Zhu | year=2006}} *{{cite journal |last1=Chow |first1=Bennett |title=The Ricci flow on the 2-sphere |journal=J. Differential Geom. |date=1991 |volume=33 |issue=2 |pages=325–334|mr=1094458|doi=10.4310/jdg/1214446319|zbl=0734.53033|doi-access=free }} *{{cite journal|last1=Colding|first1=Tobias H.|last2=Minicozzi|first2=William P. II|s2cid=2810043|title=Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman|journal=J. Amer. Math. Soc.|volume=18|year=2005|issue=3|pages=561–569|doi=10.1090/S0894-0347-05-00486-8|mr=2138137|author1-link=Tobias Colding|author2-link=William Minicozzi II|arxiv=math/0308090|jstor=20161247|url=https://www.ams.org/journals/jams/2005-18-03/S0894-0347-05-00486-8/S0894-0347-05-00486-8.pdf}} *{{cite journal|author-link=Richard S. Hamilton|last1=Hamilton|first1=Richard S.|title=Three-manifolds with positive Ricci curvature|journal=Journal of Differential Geometry|volume=17|date=1982|issue=2|pages=255–306|mr=0664497|doi=10.4310/jdg/1214436922|zbl=0504.53034|doi-access=free}} *{{cite journal |author-link=Richard S. Hamilton|last1=Hamilton |first1=Richard S. |title=Four-manifolds with positive curvature operator |journal=J. Differential Geom. |date=1986 |volume=24 |issue=2 |pages=153–179|mr=0862046|doi=10.4310/jdg/1214440433|zbl=0628.53042|doi-access=free }} *{{cite conference |last1=Hamilton|author-link=Richard S. Hamilton |first1=Richard S. |title=The Ricci flow on surfaces |book-title=Mathematics and general relativity (Santa Cruz, CA, 1986) |year=1988 |pages=237–262 |doi=10.1090/conm/071/954419|series=Contemp. Math.|volume=71 |publisher=Amer. Math. Soc., Providence, RI|mr=0954419}} *{{cite journal |last1=Hamilton|author-link=Richard S. Hamilton |first1=Richard S. |title=The Harnack estimate for the Ricci flow |journal=J. Differential Geom. |date=1993a |volume=37 |issue=1 |pages=225–243|mr=1198607|doi=10.4310/jdg/1214453430|zbl=0804.53023|doi-access=free }} *{{cite journal |last1=Hamilton|author-link=Richard S. Hamilton |first1=Richard S. |title=Eternal solutions to the Ricci flow |journal=J. Differential Geom. |date=1993b |volume=38 |issue=1 |pages=1–11|mr=1231700|doi=10.4310/jdg/1214454093|zbl=0792.53041|doi-access=free }} *{{cite journal |author-link=Richard S. Hamilton|last1=Hamilton |first1=Richard S. |title=A compactness property for solutions of the Ricci flow |journal=Amer. J. Math. |date=1995a |volume=117 |issue=3 |pages=545–572|mr=1333936|doi=10.2307/2375080|jstor=2375080}} *{{cite conference|book-title=Surveys in differential geometry, Vol. II (Cambridge, MA, 1993) |first=Richard S. |author-link=Richard S. Hamilton|publisher=Int. Press, Cambridge, MA|last=Hamilton |title=The formation of singularities in the Ricci flow |pages=7–136 |year=1995b|mr=1375255|doi=10.4310/SDG.1993.v2.n1.a2|doi-access=free}} *{{cite journal |author-link=Richard S. Hamilton|last1=Hamilton |first1=Richard S. |title=Four-manifolds with positive isotropic curvature|journal=Comm. Anal. Geom.|volume=5|issue=1|year=1997|pages=1–92|mr=1456308|doi=10.4310/CAG.1997.v5.n1.a1|zbl=0892.53018|doi-access=free}} *{{cite journal |author-link=Richard S. Hamilton|last1=Hamilton |first1=Richard S. |title=Non-singular solutions of the Ricci flow on three-manifolds|journal=Comm. Anal. Geom.|volume=7|issue=4|year=1999|pages=695–729|mr=1714939|doi=10.4310/CAG.1999.v7.n4.a2|doi-access=free}} *{{cite journal |arxiv=math.DG/0605667 |author1=Bruce Kleiner |author2-link=John Lott (mathematician) |author2=John Lott |s2cid=119133773 |title=Notes on Perelman's papers |year=2008 |doi=10.2140/gt.2008.12.2587 |volume=12 |issue=5 |journal= Geometry & Topology|pages=2587–2855|author1-link=Bruce Kleiner|mr=2460872}} *{{cite arXiv |last=Perelman |first=Grisha |author-link=Grigori Perelman |eprint=math/0211159 |title=The entropy formula for the Ricci flow and its geometric applications |date=2002 }} *{{cite arXiv |last=Perelman |first=Grisha |author-link=Grigori Perelman|eprint=math/0303109 |title=Ricci flow with surgery on three-manifolds |date=2003a }} *{{cite arXiv |last=Perelman |first=Grisha |author-link=Grigori Perelman|eprint=math/0307245 |title=Finite extinction time for the solutions to the Ricci flow on certain three-manifolds |date=2003b }}
Edit summary
(Briefly describe your changes)
By publishing changes, you agree to the
Terms of Use
, and you irrevocably agree to release your contribution under the
CC BY-SA 4.0 License
and the
GFDL
. You agree that a hyperlink or URL is sufficient attribution under the Creative Commons license.
Cancel
Editing help
(opens in new window)