Geometry & Topology Volume 12, issue 5 (2008)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Width and finite extinction time of Ricci flow

Tobias H Colding and William P Minicozzi II

Geometry & Topology 12 (2008) 2537–2586

DOI: 10.2140/gt.2008.12.2537

Bibliography

1	L Ahlfors, L Bers, Riemann's mapping theorem for variable metrics, Ann. of Math. $(2)$ 72 (1960) 385 MR0115006
2	F J Almgren, The theory of varifolds, Mimeographed notes, Princeton (1965)
3	G D Birkhoff, Dynamical systems with two degrees of freedom, Trans. Amer. Math. Soc. 18 (1917) 199 MR1501070
4	G D Birkhoff, Dynamical systems, American Math. Soc. Coll. Publ. IX, American Mathematical Society (1927) MR0209095
5	T H Colding, C De Lellis, The min-max construction of minimal surfaces, from: "Surveys in differential geometry, Vol. VIII (Boston, MA, 2002)", Int. Press (2003) 75 MR2039986
6	T H Colding, C De Lellis, W P Minicozzi II, Three circles theorems for Schrödinger operators on cylindrical ends and geometric applications, Comm. Pure Appl. Math. 61 (2008) 1540
7	T H Colding, W P Minicozzi II, Minimal surfaces, Courant Lecture Notes in Math. 4, New York University Courant Inst. of Math. Sciences (1999) MR1683966
8	T H Colding, W P Minicozzi II, Estimates for the extinction time for the Ricci flow on certain $3$–manifolds and a question of Perelman, J. Amer. Math. Soc. 18 (2005) 561 MR2138137
9	T H Colding, W P Minicozzi II, Width and mean curvature flow, Geom. Topol. 12 (2008) 2517
10	C B Croke, Area and the length of the shortest closed geodesic, J. Differential Geom. 27 (1988) 1 MR918453
11	L C Evans, Partial differential equations, Graduate Studies in Math. 19, Amer. Math. Soc. (1998) MR1625845
12	M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
13	R S Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982) 255 MR664497
14	R S Hamilton, The formation of singularities in the Ricci flow, from: "Surveys in differential geometry, Vol. II (Cambridge, MA, 1993)", Int. Press (1995) 7 MR1375255
15	F Hélein, Régularité des applications faiblement harmoniques entre une surface et une variété riemannienne, C. R. Acad. Sci. Paris Sér. I Math. 312 (1991) 591 MR1101039
16	F Hélein, Harmonic maps, conservation laws and moving frames, Cambridge Tracts in Math. 150, Cambridge University Press (2002) MR1913803
17	J Jost, Two-dimensional geometric variational problems, Pure and Applied Math. (New York), Wiley-Interscience Publ. John Wiley & Sons Ltd. (1991) MR1100926
18	B Kleiner, J Lott, Notes on Perelman's papers, Geom. Topol. 12 (2008) 2587
19	C B Morrey Jr., On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43 (1938) 126 MR1501936
20	C B Morrey Jr., Multiple integrals in the calculus of variations, Die Grund. der math. Wissenschaften 130, Springer (1966) MR0202511
21	J R Munkres, Topology: a first course, Prentice-Hall (1975) MR0464128
22	T H Parker, Bubble tree convergence for harmonic maps, J. Differential Geom. 44 (1996) 595 MR1431008
23	T H Parker, J G Wolfson, Pseudo-holomorphic maps and bubble trees, J. Geom. Anal. 3 (1993) 63 MR1197017
24	G Perelman, Ricci flow with surgery on three-manifolds arXiv:math.DG/0303109
25	G Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds arXiv:math.DG/0307245
26	J T Pitts, Existence and regularity of minimal surfaces on Riemannian manifolds, Math. Notes 27, Princeton University Press (1981) MR626027
27	J Qing, Boundary regularity of weakly harmonic maps from surfaces, J. Funct. Anal. 114 (1993) 458 MR1223710
28	T Rivière, Conservation laws for conformally invariant variational problems, Invent. Math. 168 (2007) 1 MR2285745
29	H L Royden, Real analysis, The Macmillan Co. (1963) MR0151555
30	J Sacks, K Uhlenbeck, The existence of minimal immersions of $2$–spheres, Ann. of Math. $(2)$ 113 (1981) 1 MR604040
31	J H Sampson, Some properties and applications of harmonic mappings, Ann. Sci. École Norm. Sup. $(4)$ 11 (1978) 211 MR510549
32	R Schoen, K Uhlenbeck, A regularity theory for harmonic maps, J. Differential Geom. 17 (1982) 307 MR664498
33	R Schoen, K Uhlenbeck, Boundary regularity and the Dirichlet problem for harmonic maps, J. Differential Geom. 18 (1983) 253 MR710054
34	R Schoen, J Wolfson, Minimizing area among Lagrangian surfaces: the mapping problem, J. Differential Geom. 58 (2001) 1 MR1895348
35	R Schoen, S T Yau, Lectures on harmonic maps, Conference Proceedings and Lecture Notes in Geometry and Topology, II, International Press (1997) MR1474501
36	H A Schwarz, Über einen Grenzübergang durch altirneirendes Verfahren, Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich 15 (1870) 272
37	H A Schwarz, Gesammelete Mathematische Abhandlungen, Springer (1890)
38	M Struwe, On the evolution of harmonic mappings of Riemannian surfaces, Comment. Math. Helv. 60 (1985) 558 MR826871
39	H C Wente, An existence theorem for surfaces of constant mean curvature, J. Math. Anal. Appl. 26 (1969) 318 MR0243467