A best constant and the Gaussian curvature
Author:
Chong Wei Hong
Journal:
Proc. Amer. Math. Soc. 97 (1986), 737-747
MSC:
Primary 58G30; Secondary 35B45, 53C20, 58E99
DOI:
https://doi.org/10.1090/S0002-9939-1986-0845999-7
MathSciNet review:
845999
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: For axisymmetric we find conditions to make
the scalar curvature of a metric pointwise conformal to the standard metric of
. Closely related to these results, we prove that in the inequality (Moser [8])


- [1] S. T. Yau, Survey on partial differential equations in differential geometry, Seminar on Differential Geometry (S. T. Yau ed.), Princeton Univ. Press, Princeton, N. J., 1982, pp. 3-71. MR 645729 (83i:53003)
- [2] Th. Aubin, Nonlinear analysis on manifolds, Monge-Ampere Equations, Springer-Verlag, New York, 1982. MR 681859 (85j:58002)
- [3] J. Kazdan, Gaussian and scalar curvature, an update, Seminar on Differential Geometry (S. T. Yau, ed.), Princeton Univ. Press, Princeton, N. J., 1982, pp. 185-191.
- [4] J. Moser, On a nonlinear problem in differential geometry, Dynamical Systems (M. Peixoto ed.), Academic Press, New York, 1973. MR 0339258 (49:4018)
- [5] J. Kazdan and F. Warner, Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvature, Ann. of Math. (2) 101 (1975), 317-331. MR 0375153 (51:11349)
- [6] Th. Aubin, Meilleures constantes dans le théorème d'inclusion de Sobolev, J. Funct. Anal. 32 (1979), 148-174. MR 534672 (80i:58043)
- [7]
J. Kazdan and F. Warner, Curvature functions for compact
-manifolds, Ann. of Math. (2) 99 (1974), 14-47. MR 0343205 (49:7949)
- [8]
J. Moser, A sharp form of an inequality of
. Trudinger, Indiana Univ. Math. J. 20 (1971), 1077-1092. MR 0301504 (46:662)
- [9] H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 437-477. MR 709644 (84h:35059)
- [10] E. Kamke, Differentialgleichungen, Lösungsmethoden und Lösungen. I, Gewöhnliche Differentialgleichungen, Akademische Verlagsgesellschaft, Leipzig, 1967.
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58G30, 35B45, 53C20, 58E99
Retrieve articles in all journals with MSC: 58G30, 35B45, 53C20, 58E99
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1986-0845999-7
Keywords:
Gaussian curvature,
semilinear elliptic equation
Article copyright:
© Copyright 1986
American Mathematical Society