Curvature functions for 2manifolds with negative Euler characteristic
Authors:
Jerry L. Kazdan and F. W. Warner
Journal:
Bull. Amer. Math. Soc. 78 (1972), 570574
MSC (1970):
Primary 35J25, 35J60, 53A90, 53C99; Secondary 35R05, 58G99, 47H15, 53C20
MathSciNet review:
0320947
Fulltext PDF
References 
Similar Articles 
Additional Information
 1.
Donald
S. Cohen, Multiple stable solutions of nonlinear boundary value
problems arising in chemical reactor theory, SIAM J. Appl. Math.
20 (1971), 1–13. MR 0274848
(43 #606)
 2.
R. Courant, Methods of mathematical physics. Vol. II: Partial differential equations, Interscience, New York, 1962. MR 25 # 4216.
 3.
Herman
Gluck, The generalized Minkowski problem in differential geometry
in the large, Ann. of Math. (2) 96 (1972),
245–276. MR 0309021
(46 #8132)
 4.
Jerry L. Kazdan and F. W. Warner, Integrability conditions for Δu = k  Ke, Bull. Amer. Math. Soc. 77 (1971), 819823.
 5.
Jerry
L. Kazdan and F.
W. Warner, Curvature functions for 2manifolds, Partial
differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ.
California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I.,
1973, pp. 387–392. MR 0343207
(49 #7951)
 6.
Jerry
L. Kazdan and F.
W. Warner, Curvature functions for 2manifolds, Partial
differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ.
California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I.,
1973, pp. 387–392. MR 0343207
(49 #7951)
 7.
Jerry
L. Kazdan and F.
W. Warner, Curvature functions for 2manifolds, Partial
differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ.
California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I.,
1973, pp. 387–392. MR 0343207
(49 #7951)
 8.
Jerry
L. Kazdan and F.
W. Warner, Scalar curvature and conformal deformation of Riemannian
structure, J. Differential Geometry 10 (1975),
113–134. MR 0365409
(51 #1661)
 9.
Jerry L. Kazdan and F. W. Warner, Remarks on some nonlinear elliptic equations (to appear).
 10.
M.
A. Krasnosel′skiĭ, Positive solutions of operator
equations, Translated from the Russian by Richard E. Flaherty; edited
by Leo F. Boron, P. Noordhoff Ltd. Groningen, 1964. MR 0181881
(31 #6107)
 11.
J.
Moser, On a nonlinear problem in differential geometry,
Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971) Academic
Press, New York, 1973, pp. 273–280. MR 0339258
(49 #4018)
 12.
D.
H. Sattinger, Monotone methods in nonlinear elliptic and parabolic
boundary value problems, Indiana Univ. Math. J. 21
(1971/72), 979–1000. MR 0299921
(45 #8969)
 13.
R.
Bruce Simpson and Donald
S. Cohen, Positive solutions of nonlinear elliptic eigenvalue
problems, J. Math. Mech. 19 (1969/70), 895–910.
MR
0435566 (55 #8525)
 1.
 Donald S. Cohen, Multiple stable solutions of nonlinear boundary value problems arising in chemical reactor theory, SIAM J. Appl. Math. 20 (1971), 113. MR 274848
 2.
 R. Courant, Methods of mathematical physics. Vol. II: Partial differential equations, Interscience, New York, 1962. MR 25 # 4216.
 3.
 H. Gluck, The generalized Minkowski problem in differential geometry in the large, Ann. of Math, (to appear). MR 309021
 4.
 Jerry L. Kazdan and F. W. Warner, Integrability conditions for Δu = k  Ke, Bull. Amer. Math. Soc. 77 (1971), 819823.
 5.
 Jerry L. Kazdan and F. W. Warner, Curvature functions for 2 manifolds. I (to appear). MR 343207
 6.
 Jerry L. Kazdan and F. W. Warner, Curvature functions for 2 manifolds. II (to appear). MR 343207
 7.
 Jerry L. Kazdan and F. W. Warner, Curvature functions for 2 manifolds. III. The negative Euler characteristic case (to appear). MR 343207
 8.
 Jerry L. Kazdan and F. W. Warner, Scalar curvature and conformal deformation of Riemannian structure (to appear). MR 365409
 9.
 Jerry L. Kazdan and F. W. Warner, Remarks on some nonlinear elliptic equations (to appear).
 10.
 M. A. Krasnoselskiĭ, Positive solutions of operator equations, P. Noordhoff Ltd., 1964 (translated from the 1960 Russian edition), see especially Chapter 4. MR 181881
 11.
 J. Moser, On a nonlinear problem in differential geometry (to appear). MR 339258
 12.
 D. H. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems (to appear). MR 299921
 13.
 R. B. Simpson and Donald S. Cohen, Positive solutions of nonlinear elliptic eigenvalue problems, J. Math. Mech. 19 (1970), 895910. MR 435566
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Additional Information
DOI:
http://dx.doi.org/10.1090/S000299041972130064
PII:
S 00029904(1972)130064
