Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Scalar curvatures on $ S\sp 2$


Authors: Wen Xiong Chen and Wei Yue Ding
Journal: Trans. Amer. Math. Soc. 303 (1987), 365-382
MSC: Primary 35J60; Secondary 49A40, 53C20, 58G30
MathSciNet review: 896027
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A theorem for the existence of solutions of the nonlinear elliptic equation $ - \Delta u + 2 = R(x){e^u},\;x \in {S^2}$, is proved by using a "mass center" analysis technique and by applying a continuous "flow" in $ {H^1}({S^2})$ controlled by $ \nabla R$.


References [Enhancements On Off] (What's this?)

  • [1] S. T. Yau, Survey on partial differential equations in differential geometry, Seminar on Differential Geometry, Princeton Univ., 1982, pp. 3-71. MR 645729 (83i:53003)
  • [2] J. Kazdan and F. Warner, Curvature functions for compact two manifolds, Ann. of Math. (2) 99 (1974), 14-47. MR 0343205 (49:7949)
  • [3] J. Kazdan, Prescribing the curvature of a Riemannian manifold, 1984. MR 787227 (86h:53001)
  • [4] J. Moser, On a nonlinear problem in differential geometry, Dynamical Systems, Academic Press, New York, 1973. MR 0339258 (49:4018)
  • [5] Hong Chongwei, A best constant and the Gaussian curvature (to appear). MR 845999 (87k:58284)
  • [6] Wenxiong Chen and Weiyue Ding, A problem concerning the scalar curvature on $ {S^2}$, Kexue Tongbao (to appear).
  • [7] Shi Shuzhong, Ekeland variational principle and it's applications, Preprint.
  • [8] T. Aubin, Nonlinear analysis on manifolds, Monge-Ampere equations, Springer-Verlag, 1982. MR 681859 (85j:58002)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35J60, 49A40, 53C20, 58G30

Retrieve articles in all journals with MSC: 35J60, 49A40, 53C20, 58G30


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0896027-4
PII: S 0002-9947(1987)0896027-4
Article copyright: © Copyright 1987 American Mathematical Society