Type II collapsing of maximal solutions to the Ricci flow in R 2

P. Daskalopoulos; Manuel del Pino

Annales de l'I.H.P. Analyse non linéaire (2007)

  • Volume: 24, Issue: 6, page 851-874
  • ISSN: 0294-1449

How to cite

top

Daskalopoulos, P., and 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 24.6 (2007): 851-874. <http://eudml.org/doc/78766>.

@article{Daskalopoulos2007,
author = {Daskalopoulos, P., del Pino, Manuel},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {radially symmetric initial data; soliton cigar solution; logarithmic cusp},
language = {eng},
number = {6},
pages = {851-874},
publisher = {Elsevier},
title = {Type II collapsing of maximal solutions to the Ricci flow in $\{R\}^\{2\}$},
url = {http://eudml.org/doc/78766},
volume = {24},
year = {2007},
}

TY - JOUR
AU - Daskalopoulos, P.
AU - del Pino, Manuel
TI - Type II collapsing of maximal solutions to the Ricci flow in ${R}^{2}$
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2007
PB - Elsevier
VL - 24
IS - 6
SP - 851
EP - 874
LA - eng
KW - radially symmetric initial data; soliton cigar solution; logarithmic cusp
UR - http://eudml.org/doc/78766
ER -

References

top
  1. [1] Angenent S., The zero set of a solution of a parabolic equation, J. Reine Angew. Math.390 (1988) 79-96. Zbl0644.35050MR953678
  2. [2] Angenent S., Velazquez J.J.L., Degenerate neckpinches in mean curvature flow, J. Reine Angew. Math.482 (1997) 15-66. Zbl0866.58055MR1427656
  3. [3] Bertozzi A.L., The mathematics of moving contact lines in thin liquid films, Notices Amer. Math. Soc.45 (6) (1998) 689-697. Zbl0917.35100MR1627165
  4. [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. Zbl0863.76017MR1371925
  5. [5] Chow B., The Ricci flow on the 2-sphere, J. Differential Geom.33 (2) (1991) 325-334. Zbl0734.53033MR1094458
  6. [6] de Gennes P.G., Wetting: statics and dynamics, Rev. Modern Phys.57 (3) (1985) 827-863. 
  7. [7] P. Daskalopoulos, N. Sesum, Eternal solutions to the Ricci flow in R 2 , preprint. Zbl1127.53057
  8. [8] Daskalopoulos P., del Pino M.A., On a singular diffusion equation, Comm. Anal. Geom.3 (1995) 523-542. Zbl0851.35072MR1371208
  9. [9] Daskalopoulos P., Hamilton R., Geometric estimates for the logarithmic fast diffusion equation, Comm. Anal. Geom.12 (1–2) (2004) 143-164. Zbl1070.53041
  10. [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. Zbl1065.35002MR2020328
  11. [11] Hamilton R., Eternal solutions to the Ricci flow, J. Differential Geom.38 (1993) 1-11. Zbl0792.53041MR1231700
  12. [12] Hamilton R., The Ricci flow on surfaces, in: Contemp. Math., vol. 71, Amer. Math. Soc., Providence, RI, 1988, pp. 237-262. Zbl0663.53031MR954419
  13. [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. Zbl0867.53030MR1375255
  14. [14] Hsu S.-Y., Asymptotic profile of solutions of a singular diffusion equation as t , Nonlinear Anal. Ser. A: Theory Methods48 (6) (2002) 781-790. Zbl1019.35055MR1879074
  15. [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. Zbl1053.53045MR1810206
  16. [16] Hsu S.-Y., Asymptotic behavior of solutions of the equation u t = Δ log u near the extinction time, Adv. Differential Equations8 (2) (2003) 161-187. Zbl1028.35079MR1948043
  17. [17] Hsu S.Y., Behaviour of solutions of a singular diffusion equation near the extinction time, Nonlinear Anal.56 (1) (2004) 63-104. Zbl1232.35085MR2031436
  18. [18] King J.R., Self-similar behavior for the equation of fast nonlinear diffusion, Philos. Trans. R. Soc. London Ser. A343 (1993) 337-375. Zbl0797.35097
  19. [19] Rodriguez A., Vazquez J.L., Esteban J.R., The maximal solution of the logarithmic fast diffusion equation in two space dimensions, Adv. Differential Equations2 (6) (1997) 867-894. Zbl1023.35515MR1606339
  20. [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. Zbl0780.58009MR1164949
  21. [21] Wu L.-F., The Ricci flow on complete R 2 , Comm. Anal. Geom.1 (1993) 439-472. Zbl0854.58011MR1266475

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.