Type II collapsing of maximal solutions to the Ricci flow in R 2
Daskalopoulos, P. ; del Pino, Manuel
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007), p. 851-874 / Harvested from Numdam
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@article{AIHPC_2007__24_6_851_0,
     author = {Daskalopoulos, P. and Del Pino, Manuel},
     title = {Type II collapsing of maximal solutions to the Ricci flow in ${R}^{2}$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {24},
     year = {2007},
     pages = {851-874},
     doi = {10.1016/j.anihpc.2006.06.006},
     mrnumber = {2371109},
     zbl = {pre05247888},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2007__24_6_851_0}
}

Daskalopoulos, P.; del Pino, Manuel. Type II collapsing of maximal solutions to the Ricci flow in ${R}^{2}$. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) pp. 851-874. doi : 10.1016/j.anihpc.2006.06.006. http://gdmltest.u-ga.fr/item/AIHPC_2007__24_6_851_0/

[1] Angenent S., The zero set of a solution of a parabolic equation, J. Reine Angew. Math. 390 (1988) 79-96. | MR 953678 | Zbl 0644.35050

[2] Angenent S., Velazquez J.J.L., Degenerate neckpinches in mean curvature flow, J. Reine Angew. Math. 482 (1997) 15-66. | MR 1427656 | Zbl 0866.58055

[3] Bertozzi A.L., The mathematics of moving contact lines in thin liquid films, Notices Amer. Math. Soc. 45 (6) (1998) 689-697. | MR 1627165 | Zbl 0917.35100

[4] Bertozzi A.L., Pugh M., The lubrication approximation for thin viscous films: regularity and long-time behavior of weak solutions, Comm. Pure Appl. Math. 49 (2) (1996) 85-123. | MR 1371925 | Zbl 0863.76017

[5] Chow B., The Ricci flow on the 2-sphere, J. Differential Geom. 33 (2) (1991) 325-334. | MR 1094458 | Zbl 0734.53033

[6] De Gennes P.G., Wetting: statics and dynamics, Rev. Modern Phys. 57 (3) (1985) 827-863.

[7] P. Daskalopoulos, N. Sesum, Eternal solutions to the Ricci flow in R 2 , preprint. | Zbl 1127.53057

[8] Daskalopoulos P., Del Pino M.A., On a singular diffusion equation, Comm. Anal. Geom. 3 (1995) 523-542. | MR 1371208 | Zbl 0851.35072

[9] Daskalopoulos P., Hamilton R., Geometric estimates for the logarithmic fast diffusion equation, Comm. Anal. Geom. 12 (1-2) (2004) 143-164. | Zbl 1070.53041

[10] Galaktionov V.A., Vazquez J.L., A Stability Technique for Evolution Partial Differential Equations. A Dynamical Systems Approach, Progress in Nonlinear Differential Equations and their Applications, vol. 56, Birkhäuser Boston, Boston, MA, 2004. | MR 2020328 | Zbl 1065.35002

[11] Hamilton R., Eternal solutions to the Ricci flow, J. Differential Geom. 38 (1993) 1-11. | MR 1231700 | Zbl 0792.53041

[12] Hamilton R., The Ricci flow on surfaces, in: Contemp. Math., vol. 71, Amer. Math. Soc., Providence, RI, 1988, pp. 237-262. | MR 954419 | Zbl 0663.53031

[13] Hamilton R., The formation of singularities in the Ricci flow, in: Surveys in Differential Geometry, vol. II, Internat. Press, Cambridge, MA, 1995, pp. 7-136. | MR 1375255 | Zbl 0867.53030

[14] Hsu S.-Y., Asymptotic profile of solutions of a singular diffusion equation as t→∞, Nonlinear Anal. Ser. A: Theory Methods 48 (6) (2002) 781-790. | MR 1879074 | Zbl 1019.35055

[15] Hsu S.-Y., Large time behaviour of solutions of the Ricci flow equation on R 2 , Pacific J. Math. 197 (1) (2001) 25-41. | MR 1810206 | Zbl 1053.53045

[16] Hsu S.-Y., Asymptotic behavior of solutions of the equation u t =Δ log u near the extinction time, Adv. Differential Equations 8 (2) (2003) 161-187. | MR 1948043 | Zbl 1028.35079

[17] Hsu S.Y., Behaviour of solutions of a singular diffusion equation near the extinction time, Nonlinear Anal. 56 (1) (2004) 63-104. | MR 2031436 | Zbl pre02037219

[18] King J.R., Self-similar behavior for the equation of fast nonlinear diffusion, Philos. Trans. R. Soc. London Ser. A 343 (1993) 337-375. | Zbl 0797.35097

[19] Rodriguez A., Vazquez J.L., Esteban J.R., The maximal solution of the logarithmic fast diffusion equation in two space dimensions, Adv. Differential Equations 2 (6) (1997) 867-894. | MR 1606339 | Zbl 1023.35515

[20] Wu L.-F., A new result for the porous medium equation derived from the Ricci flow, Bull. Amer. Math. Soc. 28 (1993) 90-94. | MR 1164949 | Zbl 0780.58009

[21] Wu L.-F., The Ricci flow on complete R 2 , Comm. Anal. Geom. 1 (1993) 439-472. | MR 1266475 | Zbl 0854.58011