Exotic solutions of the conformal scalar curvature equation in Rn

Man Chun Leung

Annales de l'I.H.P. Analyse non linéaire (2001)

  • Volume: 18, Issue: 3, page 297-307
  • ISSN: 0294-1449

How to cite

top

Leung, Man Chun. "Exotic solutions of the conformal scalar curvature equation in Rn." Annales de l'I.H.P. Analyse non linéaire 18.3 (2001): 297-307. <http://eudml.org/doc/78522>.

@article{Leung2001,
author = {Leung, Man Chun},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {gluing solutions; positive scalar curvature},
language = {eng},
number = {3},
pages = {297-307},
publisher = {Elsevier},
title = {Exotic solutions of the conformal scalar curvature equation in Rn},
url = {http://eudml.org/doc/78522},
volume = {18},
year = {2001},
}

TY - JOUR
AU - Leung, Man Chun
TI - Exotic solutions of the conformal scalar curvature equation in Rn
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2001
PB - Elsevier
VL - 18
IS - 3
SP - 297
EP - 307
LA - eng
KW - gluing solutions; positive scalar curvature
UR - http://eudml.org/doc/78522
ER -

References

top
  1. [1] Bahri A, Coron J, The scalar-curvature problem on standard three-dimensional sphere, J. Func. Anal.95 (1991) 106-172. Zbl0722.53032MR1087949
  2. [2] Caffarelli L, Gidas B, Spruck J, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math.42 (1989) 271-297. Zbl0702.35085MR982351
  3. [3] Chang K.-C, Liu J.-Q, On Nirenberg's problem, Internat. J. Math.4 (1993) 35-58. Zbl0786.58010MR1209959
  4. [4] Chang S.-Y, Yang P, A perturbation result in prescribing scalar curvature on Sn, Duke Math. J.64 (1991) 27-69. Zbl0739.53027MR1131392
  5. [5] Chen C.-C, Lin C.-S, On compactness and completeness of conformal metrics in RN, Asian J. Math.1 (1997) 549-559. Zbl0901.53027MR1604918
  6. [6] Chen C.-C, Lin C.-S, Estimates of the conformal scalar curvature equation via the method of moving planes, Comm. Pure Appl. Math.50 (1997) 971-1019. Zbl0958.35013MR1466584
  7. [7] Chen C.-C, Lin C.-S, Estimates of the conformal scalar curvature equation via the method of moving planes. II, J. Differential Geom.49 (1998) 115-178. Zbl0961.35047MR1642113
  8. [8] Chen C.-C, Lin C.-S, On the asymptotic symmetry of singular solutions of the scalar curvature equations, Math. Ann.313 (1999) 229-245. Zbl0927.35034MR1679784
  9. [9] Chen W.-X, Li C.-M, A necessary and sufficient condition for the Nirenberg problem, Comm. Pure Appl. Math.48 (1995) 657-667. Zbl0830.35034MR1338474
  10. [10] Cheung K.-L, Leung M.-C, Asymptotic behavior of positive solutions of the equation Δu+Ku(n+2)/(n−2)=0 in Rn and positive scalar curvature, in: Discrete Contin. Dynam. Systems, Added Volume, Proceedings of the International Conference on Dynamical Systems and Differential Equations, 2001, pp. 109-120. 
  11. [11] Delaunay C, Sur la surface de revolution dont la courbure moyenne est constante, J. de Mathématiques6 (1841) 309-320. 
  12. [12] Ding W.-Y, Ni W.-M, On the elliptic equation Δu+Ku(n+2)/(n−2)=0 and related topics, Duke Math. J.52 (1985) 485-506. Zbl0592.35048
  13. [13] Fowler R, Further studies of Emden's and similar differential equations, Quart. J. Math. Oxford Ser.2 (1931) 259-288. Zbl0003.23502
  14. [14] Gidas B, Ni W.-M, Nirenberg L, Symmetry and related properties via the maximum principle, Comm. Math. Phys.68 (1979) 209-243. Zbl0425.35020MR544879
  15. [15] Gidas B, Ni W.-M, Nirenberg L, Symmetry of positive solutions of nonlinear elliptic equations in Rn, in: Mathematical Analysis and Applications, Part A, Adv. in Math. Suppl. Stud., 7a, Academic Press, New York, 1981, pp. 369-402. Zbl0469.35052MR634248
  16. [16] Korevaar N, Mazzeo R, Pacard F, Schoen R, Refined asymptotics for constant scalar curvature metrics with isolated singularities, Invent. Math.135 (1999) 233-272. Zbl0958.53032MR1666838
  17. [17] Leung M.-C, Conformal scalar curvature equations on complete manifolds, Comm. Partial Differential Equations20 (1995) 367-417. Zbl0833.53038MR1318076
  18. [18] Leung M.-C, Asymptotic behavior of positive solutions of the equation Δgu+Kup=0 in a complete Riemannian manifold and positive scalar curvature, Comm. Partial Differential Equations24 (1999) 425-462. Zbl0939.58024
  19. [19] Leung M.-C., Growth estimates on positive solutions of the equation Δu+Ku(n+2)/(n−2)=0 in Rn, Canad. Math. Bull., to appear. Zbl0979.35046
  20. [20] Li Y.-Y, Prescribing scalar curvature on Sn and related problems, part I, J. Differential Equations120 (1995) 319-410. Zbl0827.53039MR1347349
  21. [21] Li Y.-Y, Prescribing scalar curvature on Sn and related problems, part II: existence and compactness, Comm. Pure Appl. Math.49 (1996) 541-597. Zbl0849.53031MR1383201
  22. [22] Lin C.-S, Estimates of the conformal scalar curvature equation via the method of moving planes III, Comm. Pure Appl. Math.53 (2000) 611-646. Zbl1035.53052MR1737506
  23. [23] Loewner C, Nirenberg L, Partial differential equations invariant under conformal or projective transformations, in: Contributions to Analysis (a collection of papers dedicated to Lipman Bers), Academic Press, New York, 1974, pp. 245-272. Zbl0298.35018MR358078
  24. [24] Mazzeo R, Pacard F, Constant scalar curvature metrics with isolated singularities, Duke Math. J.99 (1999) 353-418. Zbl0945.53024MR1712628
  25. [25] Mazzeo R, Pollack D, Uhlenbeck K, Moduli spaces of singular Yamabe metrics, J. Amer. Math. Soc.9 (1996) 303-344. Zbl0849.58012MR1356375
  26. [26] Schoen R, The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation, Comm. Pure Appl. Math.41 (1988) 317-392. Zbl0674.35027MR929283
  27. [27] Taliaferro S, On the growth of superharmonic functions near an isolated singularity, I., J. Differential Equations158 (1999) 28-47. Zbl0939.31005MR1721720

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.